Department of STATISTICS 

Syllabus for

1 Semester  2021  Batch  
Course Code 
Course 
Type 
Hours Per Week 
Credits 
Marks 
MST131  PROBABILITY THEORY    5  5  100 
MST132  DISTRIBUTION THEORY    5  5  100 
MST133  MATRIX THEORY AND LINEAR MODELS    5  5  100 
MST134  RESEARCH METHODOLOGY AND LATEX    2  2  50 
MST171  SAMPLE SURVEY DESIGNS    6  5  150 
MST172  STATISTICAL COMPUTING USING R    5  4  150 
2 Semester  2021  Batch  
Course Code 
Course 
Type 
Hours Per Week 
Credits 
Marks 
MST231  STATISTICAL INFERENCEI    4  4  100 
MST232  STOCHASTIC PROCESSES    4  4  100 
MST233  CATEGORICAL DATA ANALYSIS    4  4  100 
MST271  REGRESSION ANALYSIS    6  5  150 
MST272  STATISTICAL COMPUTING USING PYTHON    5  4  150 
MST273A  PRINCIPLES OF DATA SCIENCE AND DATA BASE TECHNIQUES    5  4  150 
MST273B  SURVIVAL ANALYSIS    5  4  150 
MST273C  OPTIMIZATION TECHNIQUES    5  4  100 
MST281  RESEARCH PROBLEM IDENTIFICATION AND FORMULATION    2  1  50 
3 Semester  2020  Batch  
Course Code 
Course 
Type 
Hours Per Week 
Credits 
Marks 
MST331  STATISTICAL INFERENCE II    4  4  100 
MST332  MULTIVARIATE ANALYSIS    4  4  100 
MST371  TIME SERIES ANALYSIS    6  5  150 
MST372A  STATISTICAL MACHINE LEARNING    5  4  150 
MST372B  BIOSTATISTICS    5  4  150 
MST372C  RELIABILITY ENGINEERING    5  4  150 
MST373A  NUMERICAL ANALYSIS    5  4  150 
MST373B  NONPARAMETRIC METHODS    5  4  150 
MST373C  THEORY OF GAMES AND STATISTICAL DECISIONS    5  4  150 
MST381  RESEARCH MODELING AND IMPLEMENTATION    8  4  200 
4 Semester  2020  Batch  
Course Code 
Course 
Type 
Hours Per Week 
Credits 
Marks 
MST431  ADVANCED OPERATIONS RESEARCH    4  4  100 
MST432  DESIGN AND ANALYSIS OF EXPERIMENTS    4  4  100 
MST433  STATISTICAL QUALITY CONTROL    4  4  100 
MST471A  NEURAL NETWORKS AND DEEP LEARNING    5  4  150 
MST471B  SPATIAL STATISTICS    5  4  150 
MST471C  BIG DATA ANALYTICS    5  4  150 
MST472A  HIGH DIMENSIONAL STATISTICAL ANALYSIS    5  4  150 
MST472B  STATISTICAL GENETICS    5  4  150 
MST472C  ACTUARIAL METHODS    5  4  150 
MST473A  BAYESIAN STATISTICS    5  4  150 
MST473B  CLINICAL TRIALS    5  4  150 
MST473C  RISK MODELING    5  4  150 
MST481  SEMINAR PRESENTATION    2  1  50 
 
Department Overview:  
Statistics is the body of scientific principles and methodologies that are used to extract useful and comprehensive information from data to draw conclusions about any phenomenon and is a discipline that studies the best ways of dealing with randomness, or more precisely and broadly, variation. The Department of Statistics is the deep interplay between application, computation and theory, as well as the backbone of data science. It renders a good combination of pure and applied statistics with software skills, enabling students to successfully participate in professional life by gaining knowledge.  
Mission Statement:  
Department Vision: The departme  
Introduction to Program:  
Master of Science in Statistics at CHRIST (Deemed to be University) offers the students an amalgam of knowledge on theoretical and applied statistics on a broader spectrum. Further, it intends to impart awareness of the importance of the conceptual framework of statistics across diversified fields and provide practical training on statistical methods for carrying out data analysis using sophisticated programming languages and statistical softwares such as R, Python, SPSS, EXCEL, etc. The course curriculum has been designed in such a way to cater for the needs of stakeholders to get placements in industries and institutions on successful completion of the course and to provide those ample skills and opportunities to meet the challenges at the national level competitive examinations like CSIR NET in Mathematical Science, SET, Indian Statistical Service (ISS) etc.  
Program Objective:  
Programme Objectives:
 
Assesment Pattern  
CIA  50% ESE  50%  
Examination And Assesments  
CIA  50% ESE  50% 
MST131  PROBABILITY THEORY (2021 Batch)  
Total Teaching Hours for Semester:75 
No of Lecture Hours/Week:5 
Max Marks:100 
Credits:5 
Course Objectives/Course Description 

Probability is a measure of uncertainty and forms the foundation of statistical methods. This course makes students use measuretheoretic and analytical techniques for understanding probability concepts. 

Learning Outcome 

By the end of the course, the learner will be able to: CO1: Relate measure and probability concepts CO2: Analyse probability concepts using the measuretheoretic approach CO3: Evaluate conditional distributions and conditional expectations CO4: Make use of limit theorems in the convergence of random variables 
Unit1 
Teaching Hours:15 

Probability and Random variable


Sets – functions  Sigma field – Measurable space – Sample space – Measure – Probability as a measure  Inverse function  Measurable functions – Random variable  Induced probability space  Distribution function of a random variable: definition and properties.  
Unit2 
Teaching Hours:15 

Expectation and Generating functions


Expectation and moments: Definition and properties – Probability generating function  Moment generating functions  Moment inequalities: Markov’s, Chebychev’s, Holder, Jenson and basic inequalities  Characteristic function and properties (idea and statement only).  
Unit3 
Teaching Hours:15 

Random Vectors


Random vectors – joint distribution function – joint moments  Conditional probabilities  RandonNikodym Theorem (Statement only)  Bayes’ theorem – conditional distributions – independence  Conditional expectation and its properties  
Unit4 
Teaching Hours:15 

Convergence


Modes of convergence: Convergence in probability, in distribution, in rth mean, almost sure convergence and their interrelationships  Convergence theorem for expectation  
Unit5 
Teaching Hours:15 

Limit theorems


Law of large numbers  Convergence of series of independent random variables  Weak law of large numbers (Kninchine’s and Kolmogorov’s)  Kolmogorov’s strong law of large numbers  Central limit theorems for i.i.d random variables: LindbergLevy and Liaponov’s CLT.  
Text Books And Reference Books:
 
Essential Reading / Recommended Reading
 
Evaluation Pattern
 
MST132  DISTRIBUTION THEORY (2021 Batch)  
Total Teaching Hours for Semester:75 
No of Lecture Hours/Week:5 

Max Marks:100 
Credits:5 

Course Objectives/Course Description 

Probability distributions are used in many reallife phenomena. This course makes students understand different probability distributions and model reallife problems using them. 

Learning Outcome 

By the end of the course, the learner will be able to: CO1: Classify different families of probability distributions. CO2: Analyse wellknown probability distributions as a special case of different families of distribution CO3: Identify different distributions arising from sampling from the normal distribution. CO4: Apply probability distribution in various statistical problems. 
Unit1 
Teaching Hours:15 

System of linear equations


Matrix operations  Linear equations  row reduced and echelon form  Homogenous system of equations  Linear dependence  
Unit2 
Teaching Hours:15 

Vector Space


Vectors  Operations on vector space  subspace  nullspace and column space  Linearly independent sets  spanning set  bases  dimension  rank  change of basis.  
Unit3 
Teaching Hours:15 

Linear transformations


Algebra of linear transformations  Matrix representations  rank nullity theorem  determinants  eigenvalues and eigenvectors  CayleyHamilton theorem  Jordan canonical forms  orthogonalisation process  orthonormal basis.  
Unit4 
Teaching Hours:15 

Quadratic forms and special matrices useful in statistics


Reduction and classification of quadratic forms  Special matrices: symmetric matrices  positive definite matrices  idempotent and projection matrices  stochastic matrices  Gramian matrices  dispersion matrices  
Unit5 
Teaching Hours:15 

Linear models


Fitting the model  ordinary least squares  estimability of parametric functions  Gauss – Markov theorem  applications: regression model  analysis of variance.  
Text Books And Reference Books:
 
Essential Reading / Recommended Reading
 
Evaluation Pattern
 
MST134  RESEARCH METHODOLOGY AND LATEX (2021 Batch)  
Total Teaching Hours for Semester:30 
No of Lecture Hours/Week:2 

Max Marks:50 
Credits:2 

Course Objectives/Course Description 

To acquaint students with different methodologies in statistical research and to make them prepare scientific articles using LaTeX. 

Learning Outcome 

By the end of the course, the learner will be able to: CO1: Define a research problem CO2: Identify suitable methodology for solving the research problem CO3: Create scientific articles using LaTeX.

Unit1 
Teaching Hours:15 
Fundamentals of research


Objectives  Motivation  Utility  Concept of theory  empiricism  deductive and inductive theory  Characteristics of the scientific method  Understanding the language of research  Concept  Construct  Definition  Variable  Research Process Problem Identification & Formulation  Research Question – Investigation Question  Logic & Importance  
Unit2 
Teaching Hours:15 
Scientific writing


Principles of mathematical writing  LaTeX: installing packages and editor, preparing title page  mathematical expressions  tables  importing graphics  bibliography  writing a research paper  survey article  thesis writing  Beamer: preparing presentations  
Text Books And Reference Books:
 
Essential Reading / Recommended Reading 1.Grätzer, G. (2013). Math into LATEX. Springer Science & Business Media.  
Evaluation Pattern CIA  50% ESE  50%  
MST171  SAMPLE SURVEY DESIGNS (2021 Batch)  
Total Teaching Hours for Semester:90 
No of Lecture Hours/Week:6 
Max Marks:150 
Credits:5 
Course Objectives/Course Description 

This course aims to impart the concepts of survey sampling theory and the analysis of complex surveys, including methods of sample selection, estimation, sampling variance, standard error of estimation in a finite population, development of sampling theory for use in sample survey problems and sources of errors in surveys. 

Learning Outcome 

By the end of the course, the learner will be able to: CO1: List different steps in designing a sample survey. CO2: Analyse different sample survey designs and find estimators. CO3: Identify the use of different sample survey designs. CO4: Apply suitable sample survey design in reallife problems. 
Unit1 
Teaching Hours:18 
Random sampling designs


Sampling vs census, simple random sampling: with (SRS) and without replacement (SRSWOR) of units, estimators of mean, total and variance, determination of sample size, sampling for proportions, Stratified sampling scheme: estimation and allocation of sample size, comparison with simple random sampling schemes. Lab Exercises: 1. Drawing samples with SRSWR and SRSWOR and estimation of parameters 2. Estimation of parameters using a sample of proportions 3. Drawing stratified sample and estimation of parameters  
Unit2 
Teaching Hours:18 
Ratio and regression estimators


Bias and mean square error, estimation of variance, confidence interval, comparison with mean per unit estimator, optimum property of ratio estimator, unbiased ratio type estimator, ratio estimator in stratified random sampling, Difference estimator and Regression estimator: Difference estimator, regression estimator, comparison of regression estimator with mean per unit and ratio estimator, regression estimator in stratified random sampling. Lab Exercises: 4. Estimation using ratio estimator 5. Estimation using regression estimator 6. Ratio estimator and regression estimator in stratified sampling  
Unit3 
Teaching Hours:18 
Varying probability sampling designs


With and without replacement sampling schemes: PPS and PPSWR schemes, Selection of samples, estimators: ordered and unordered estimators. Πps sampling schemes. Lab Exercises: 7. Exercise on the PPS scheme 8. Exercise on the PPSWR scheme 9. Exercise on Πps sampling scheme  
Unit4 
Teaching Hours:18 
Advanced sampling designs


Systematic sampling scheme: estimation of population mean and variance, comparison of systematic sampling with SRS and stratified random sampling, circular systematic sampling, Cluster sampling: estimation of population mean, estimation of efficiency by a cluster sample, variance function, determination of optimum cluster size, Multistage sampling: estimation population total with SRS sampling at both stages, multiphase sampling (outline only), quota sampling, network sampling; Adaptive sampling: introduction and estimators under adaptive sampling. Introduction to small area estimation. Lab Exercises: 9. Exercise on the systematic sampling scheme 10. Exercise on cluster sampling 11. Exercise on multistage sampling 12. Exercise on small area estimation  
Unit5 
Teaching Hours:18 
Errors in Sample Survey


Sampling and nonsampling errors, the effect of unit nonresponse in the estimate, procedures for unit nonresponse Lab Exercises: 13. Exercise on the sensitivity of efficiency due to sampling errors 14. Procedures for nonresponse  
Text Books And Reference Books: 1. Arnab, R. (2017). Survey sampling: Theory and Applications. Academic Press. 2. Singh, D. and Chaudharay, F.S. (2018) Theory and Analysis of Sample Survey Designs, New Age International.
 
Essential Reading / Recommended Reading 1. Cochran, W.G. (2007) Sampling Techniques, Third edition, John Wiley & Sons. 2. Singh, S. (2003). Advanced Sampling: Theory and Practice. Kluwer. 3. Des Raj and Chandhok, P. (2013) Sampling Theory, McGraw Hill. 4. Mukhopadhay, P (2009) Theory and methods of survey sampling, Second edition, PHI Learning Pvt Ltd., New Delhi. 5. Sampath, S. (2005) Sampling theory and methods, Alpha Science International Ltd., India. 6. Lumley, T. (2011). Complex surveys: a guide to analysis using R. John Wiley & Sons.
 
Evaluation Pattern CIA  50% ESE  50%  
MST172  STATISTICAL COMPUTING USING R (2021 Batch)  
Total Teaching Hours for Semester:75 
No of Lecture Hours/Week:5 
Max Marks:150 
Credits:4 
Course Objectives/Course Description 

The programming skill in R helps students to perform statistical computations with ease. This course equips students with knowledge of R programming to develop statistical models for realworld problems 

Learning Outcome 

By the end of the course, the learner will be able to: CO1: Demonstrate the understanding of basic concepts of R programming CO2: Build useful programs with functions CO3: Analyse various data using R. CO4: Create visualisation of data using R CO5: Compare different methods of simulating random numbers

Unit1 
Teaching Hours:15 
Introduction


R and R studio  Variables  Functions  Vectors  Expressions and assignments  Logical expressions  Matrices  The workspace  R markdown. Practical Assignments: 1. Demonstrate variables and functions in R 2. Creating vectors and matrices and associated operations in R 3. Logical and arithmetic operations in R
 
Unit2 
Teaching Hours:15 
Basic Programming


Loops: if, for, while  Program flow  Basic debugging  Good programming habits  Input and outputs: Input from a file and output to a file Practical Assignments: 4. Illustration of control structures: if, else, for 5. Illustration of control structures: while, repeat, break, next and ifelse
 
Unit3 
Teaching Hours:15 
Programming with functions


Functions  Optional arguments and default values  Vectorbased programming using functions  Recursive programming  Debugging functions  Sophisticated data structures  Factors Dataframes  Lists  The apply family. Practical Assignments: 7. Creating userdefined functions and doing vectorbased programming 8. Creating lists and data frames and associated operations 9. Demonstration of recursive functions, apply functions in R
 
Unit4 
Teaching Hours:15 
Graphics


Visualising data  Graphical summaries of data: Bar chart, Pie chart, Histogram, Boxplot, Stem and leaf plot, Frequency table  Plotting of probability distributions and sampling distributions  PP plot  QQ Plot  ggplot2  lattice – 3D plots,  par graphical augmentation. Practical Assignments: 10. Visualization of univariate data 11. Visualization of numerical variables in R using ‘base R’, ‘ggplot2’ and ‘lattice 3D’ packages 12. Contingency tables and visualization of categorical variables using ‘base R’, ‘ggplot2’ and ‘lattice 3D’ packages 13. Construction of probability plots and quantile plots in R
 
Unit5 
Teaching Hours:15 
Simulation


Simulating iid uniform samples  Congruential generators  Seeding  Simulating discrete random variables  Inversion method for continuous random variables  Rejection method  generation of normal variates: Rejection with exponential envelope, BoxMuller algorithm. Practical Assignments: 14. Simulation of discrete variables in R 15. Simulation of continuous variables inversion method, rejection method
 
Text Books And Reference Books: 1.Jones, O., Maillardet. R. and Robinson, A. (2014). Introduction to Scientific Programming and Simulation Using R. Chapman & Hall/CRC, The R Series. 2.Matloff, N. (2016). The art of R programming: A tour of statistical software design. No Starch Press.
 
Essential Reading / Recommended Reading 1.Crawley, M, J. (2012). The R Book, 2nd Edition. John Wiley & Sons. 2.Chambers, J. M. (2008). Software for Data AnalysisProgramming with R. SpringerVerlag, New York.
 
Evaluation Pattern CIA  50% ESE  50%  
MST231  STATISTICAL INFERENCEI (2021 Batch)  
Total Teaching Hours for Semester:60 
No of Lecture Hours/Week:4 
Max Marks:100 
Credits:4 
Course Objectives/Course Description 

To provide a strong mathematical and conceptual foundation in the methods of parametric estimation and their properties. 

Learning Outcome 

By the end of the course, the learner will be able to: CO1: List properties of estimators. CO2: Identify a suitable estimation method. CO3: Analyse likelihood function and apply different root solving methods to find estimators CO4: Construct confidence intervals for parameters involved in the model.

Unit1 
Teaching Hours:12 

Sufficiency


Sufficiency  factorisation theorem  minimal sufficiency  exponential family and completeness  Ancillary statistics and Basu's theorem  
Unit2 
Teaching Hours:12 

Unbiasedness


UMVUE  Fisher Information and CramerRao inequality  ChapmanRobbin’s and Bhattacharya bounds  RaoBlackwell theorem  LehmanScheffe theorem  Unbiased estimation  
Unit3 
Teaching Hours:12 

Consistent estimators


Consistency  Weak and strong consistency  Marginal and joint consistent estimators  CAN estimators  equivariance  Pitman estimators  
Unit4 
Teaching Hours:12 

Methods of point estimation


Methods of moments  Minimum chi square and its modification, Least square estimation, Maximum likelihood, Properties of maximum likelihood estimators, CramerHuzurbazar Theorem, Likelihood equation  multiple roots, Iterative methods, EM Algorithm.  
Unit5 
Teaching Hours:12 

Interval estimation


Large sample confidence interval  shortest length confidence interval  Methods of finding confidence interval: Inversion of the test statistic, pivotal quantities, pivoting CDF evaluation of confidence interval: size and coverage probability, loss function and test function optimality.  
Text Books And Reference Books:
 
Essential Reading / Recommended Reading 1.Casella, G., & Berger, R. L. (2002). Statistical inference. Pacific Grove, CA: Duxbury. 2.Silvey, S. D. (2017). Statistical inference. Routledge. 3.Trosset, M. W. (2009). An introduction to statistical inference and its applications with R. Chapman and Hall/CRC. 4.Dixit, U. J. (2016). Examples in parametric inference with R, Springer. 5.Lehmann, E. L., & Casella, G. (2006). Theory of point estimation, 2nd Ed. Springer. 6.Robert, C., & Casella, G. (2013). Monte Carlo statistical methods. Springer
 
Evaluation Pattern
 
MST232  STOCHASTIC PROCESSES (2021 Batch)  
Total Teaching Hours for Semester:60 
No of Lecture Hours/Week:4 

Max Marks:100 
Credits:4 

Course Objectives/Course Description 

To equip the students with theoretical and practical knowledge of stochastic models which are used in economics, life sciences, engineering etc. 

Learning Outcome 

By the end of the course, the learner will be able to: CO1: List different stochastic models. CO2: Identify ergodic Markov chains. CO3: Analyse queuing models using continuoustime Markov chains. CO4: Apply Brownian motion in finance problems.

Unit1 
Teaching Hours:12 

Introduction


A sequence of random variables  definition and classification of the stochastic process  autoregressive processes and Strict Sense and Wide Sense stationary processes.  
Unit2 
Teaching Hours:12 

Discrete time Markov chains


Markov Chains: Definition, Examples  Transition probability matrix  ChapmanKolmogorv equation  classification of states  limiting and stationary distributions  ergodicity  discrete renewal equation and basic limit theorem  Absorption probabilities  Criteria for recurrence  Generic application: hidden Markov models.  
Unit3 
Teaching Hours:12 

Continuous time Markov chains and Poisson process


Transition probability function  Kolmogorov differential equations  Poisson process: homogenous process, interarrival time distribution, compound process  Birth and death process  Service applications: Queuing models Markovian models.  
Unit4 
Teaching Hours:12 

Branching process


GaltonWatson branching processes  Generating function  Extinction probabilities  Continuoustime branching processes  Extinction probabilities  Branching processes with general variable lifetime.  
Unit5 
Teaching Hours:12 

Renewal process and Brownian motion


Renewal equation  Renewal theorem  Generalisations and variations of renewal processes  Brownian motion  Introduction to Markov renewal processes.  
Text Books And Reference Books: 1.Karlin, S. and Taylor, H.M. (2014). A first course in stochastic processes. Academic Press. 2.S. M. Ross (2014). Introduction to Probability Models. Elsevier.
 
Essential Reading / Recommended Reading 1.Feller, W. (2008) An Introduction to Probability Theory and its Applications, Volume I&II, 3rd Ed., Wiley Eastern. 2.J. Medhi (2009) Stochastic Processes, 3rd Edition, New Age International. 3.Dobrow, R.P. (2016), Introduction to Stochastic Processes with R, Wiley Eastern. 4.Cinlar, E. (2013). Introduction to stochastic processes. Courier Corporation.
 
Evaluation Pattern
 
MST233  CATEGORICAL DATA ANALYSIS (2021 Batch)  
Total Teaching Hours for Semester:60 
No of Lecture Hours/Week:4 

Max Marks:100 
Credits:4 

Course Objectives/Course Description 

Categorical data analysis deals with the study of information captured through expressions or verbal forms. This course equips the students with the theory and methods to analyse and categorical responses. 

Learning Outcome 

By the end of the course, the learner will be able to: CO1: Describe the categorical response. CO2: Identify tests for contingency tables. CO3: Apply regression models for categorical response variables. CO4: Analyse contingency tables using loglinear models.

Unit1 
Teaching Hours:12 

Introduction


Categorical response data  Probability distributions for categorical data  Statistical inference for discrete data  
Unit2 
Teaching Hours:12 

Contingency tables


Probability structure for contingency tables  Comparing proportions with 2x2 tables  The odds ratio  relative risk  Tests for independence  Association of IXJ tables  
Unit3 
Teaching Hours:12 

Generlaized linear models


Components of a generalised linear model  GLM for binary and count data  Statistical inference and model checking  Fitting GLMs  
Unit4 
Teaching Hours:12 

Logistic regression


Interpreting the logistic regression model  Inference for logistic regression  Logistic regression with categorical predictors  Multiple logistic regression  Summarising effects  Building and applying logistic regression models  Multicategory logit models  
Unit5 
Teaching Hours:12 

Loglinear models for contingency tables


Loglinear models for twoway and threeway tables  Inference for Loglinear models  the loglinearlogistic connection  Models for matched pairs: Comparing dependent proportions, Logistic regression for matched pairs  Comparing margins of square contingency tables  symmetry issues  
Text Books And Reference Books: 1. Agresti, A. (2012). Categorical Data Analysis, 3rd Edition. New York: Wiley 2. Agresti, A. (2010). Analysis of ordinal categorical data. John Wiley & Sons.  
Essential Reading / Recommended Reading 1. Le, C.T. (2009). Applied Categorical Data Analysis and Translational Research, 2^{nd} Ed., John Wiley and Sons. 2. Stokes, M. E., Davis, C. S., & Koch, G. G. (2012). Categorical data analysis using SAS. SAS Institute. 3. Agresti, A. (2018). An introduction to categorical data analysis. John Wiley & Sons. 4. Bilder, C. R., & Loughin, T. M. (2014). Analysis of categorical data with R. Chapman and Hall/CRC.  
Evaluation Pattern
 
MST271  REGRESSION ANALYSIS (2021 Batch)  
Total Teaching Hours for Semester:90 
No of Lecture Hours/Week:6 

Max Marks:150 
Credits:5 

Course Objectives/Course Description 

Regression models are mainly used in establishing a relationship among variables and predicting future values. It got applications in various domain such as finance, life science, management, psychology, etc. This course is designed to impart the knowledge of statistical model building using regression technique. 

Learning Outcome 

By the end of the course, the learner will be able to: CO1: Formulate simple and multiple regression models CO2: Identify the correct regression model for the given problem CO3: Apply nonlinear regression in reallife problems. CO4: Analyse the robustness of the regression model.

Unit1 
Teaching Hours:18 
Linear regression model


Linear Regression Model: Simple and multiple  Least squares estimation  Properties of the estimators  Maximum likelihood estimation  Estimation with linear restrictions  Hypothesis testing  confidence intervals. Practical Assignments: 1. Build a simple linear model and interpret the data. 2. Construct confidence interval for the simple linear model 3. Build a multiple linear models and estimate its parameters. 4. Construct confidence interval for multiple linear model
 
Unit2 
Teaching Hours:18 
Model adequacy


Residual analysis  Departures from underlying assumptions  Effect of outliers  Collinearity  Nonconstant variance and serial correlation  Departures from normality  Diagnostics and remedies. Practical Assignments: 5. Carry out residual analysis and validate the model assumptions. 6. Construct residual plots for checking outliers, leverage points and influential points. 7. Checking the assumption of homoscedasticity and its remedial measures 8. Detecting multicollinearity and its remedial measures
 
Unit3 
Teaching Hours:18 
Model Selection


selection of input variables and model selection  Methods of obtaining the best fit  stepwise regression  Forward selection and backward elimination Practical Assignments: 9. Selecting the best model using step wise regression. 10. Selecting the best model using the forward and backward selection procedure.
 
Unit4 
Teaching Hours:18 
Nonlinear regression


Introduction to general nonlinear regression  leastsquares in nonlinear case  estimating the parameters of a nonlinear system  reparametrization of the model  Nonlinear growth models Practical Assignments: 11.Estimate parameters in nonlinear models using the least square procedure
 
Unit5 
Teaching Hours:18 
Robust regression


Linear absolute deviation regression  M estimators  robust regression with rank residuals  resampling procedures for regression models, methods and its properties (without proof)  Jackknife techniques and leastsquares approach based on Mestimators. Practical Assignments: 12. Illustrate resampling procedures in regression models. 13. Build a regression model with robust regression procedures.
 
Text Books And Reference Books: 1. Chatterjee, S., & Hadi, A. S. (2015). Regression analysis by example. John Wiley & Sons. 2. Draper, N. R., & Smith, H. (2014). Applied regression analysis. 3rd edition. John Wiley & Sons. 3. Montgomery, D. C., Peck, E. A., & Vining, G. G. (2021). Introduction to linear regression analysis. John Wiley & Sons.
 
Essential Reading / Recommended Reading 1. Seber, G. A., & Lee, A. J. (2012). Linear regression analysis (Vol. 329). John Wiley & Sons. 2. Keith, T. Z. (2014). Multiple regression and beyond: An introduction to multiple regression and structural equation modelling. Routledge. 3. Fox, J. (2015). Applied regression analysis and generalized linear models. Sage Publications. 4. Fox, J., & Weisberg, S. (2018). An R companion to applied regression. Sage publications.
 
Evaluation Pattern CIA  50% ESE  50%
 
MST272  STATISTICAL COMPUTING USING PYTHON (2021 Batch)  
Total Teaching Hours for Semester:75 
No of Lecture Hours/Week:5 
Max Marks:150 
Credits:4 
Course Objectives/Course Description 

Python is a generic programming language that is extensively used in data science. This course equips students with programming skill in Python and associated statistical libraries and to apply in data analysis 

Learning Outcome 

By the end of the course, the learner will be able to: CO1: Demonstrate the understanding of the fundamentals of Python programming CO2: Implement functions and data modelling CO3: Analyze statistical datasets and visualize the results. CO4: Build statistical models using various statistical libraries in python

Unit1 
Teaching Hours:15 
Introduction


Installing Python  basic syntax  interactive shell  editing, saving and running a script. The concept of data types  variables  assignments  mutable type  immutable types  arithmetic operators and expressions  comments in the program  understanding error messages  Control statements  operators.
Practical Assignments: 1. Lab exercise on data types 2. Lab exercise on arithmetic operators and expressions 3. Lab exercise on Control statements
 
Unit2 
Teaching Hours:15 
Design with functions


Introduction to functions  inbuilt and user defined functions  functions with arguments and return values  formal vs actual arguments  named arguments  Recursive functions  Lambda function  OOP Concepts  classes  objects  attributes and methods  defining classes  inheritance  polymorphism.
Practical Assignments: 4. Lab exercise on inbuilt and userdefined functions 5. Lab exercise on Recursive and Lambda function 6. Lab exercise on OOP Concepts.
 
Unit3 
Teaching Hours:15 
Statistical Analysis I using Pandas


Introduction to Pandas  Pandas data series  Pandas data frames  data handling  grouping  Descriptive statistical analysis and Graphical representation.
Practical Assignments: 7. Lab exercise on Pandas data series, frame, handling and grouping 8. Lab exercise on statistical analysis
 
Unit4 
Teaching Hours:15 
Statistical Analysis  II using Pandas


Hypothesis testing  data modelling  linear regression models  logistic regression model.
Practical Assignments: 9. Lab exercise on Hypothesis testing 10. Lab exercise on regression modelling
 
Unit5 
Teaching Hours:15 
Visualization Using Seaborn and Matplotlib


Line graph  Bar chart  Pie chart  Heat map  Histogram  Density plot  Cumulative frequencies  Error bars  Scatter plot  3D plot.
Practical Assignments: 11. Lab exercise on graphical and diagrammatic representation. 12. Lab exercise on the density plot 13. Lab exercise on scatter and 3D plot  
Text Books And Reference Books: 1.Lambert, K. A. (2018). Fundamentals of Python: first programs. Cengage Learning. 2.Haslwanter, T. (2016). An Introduction to Statistics with Python. Springer International Publishing.
 
Essential Reading / Recommended Reading 1.Unpingco, J. (2016). Python for probability, statistics, and machine learning, Vol.1, Springer International Publishing. 2.Anthony, F. (2015). Mastering pandas. Packt Publishing Ltd.
 
Evaluation Pattern CIA  50% ESE  50%
 
MST273A  PRINCIPLES OF DATA SCIENCE AND DATA BASE TECHNIQUES (2021 Batch)  
Total Teaching Hours for Semester:75 
No of Lecture Hours/Week:5 
Max Marks:150 
Credits:4 
Course Objectives/Course Description 

This course provides a strong foundation for data science and the application area related to it and caters for the underlying core concepts and emerging technologies in data science. 

Learning Outcome 

By the end of the course, the learner will be able to: CO1: Explore the fundamental concepts of data science CO2: Apply data analysis techniques for handling large data CO3: Demonstrate various databases and Compose effective queries

Unit1 
Teaching Hours:15 
Introduction to Data Science


Introduction – Big Data and Data Science – Data science Hype – Getting Past the Hype – The Current Landscape – Role of Data Scientist – Exploratory Data Analysis – Data Science Process Overview – Defining goals – Retrieving data – Data preparation – Data exploration – Data modelling – Presentation. Problems in handling large data – General techniques for handling large data – Big Data and its importance, Four Vs, Drivers for Big data, Big data analytics, Big data applications, Algorithms using mapreduce, MatrixVector Multiplication by Map Reduce. Steps in big data – Distributing data storage and processing with Frameworks – Data science ethics – valuing different aspects of privacy – The five C’s of data. Practical Assignments 1. Lab exercise for feature engineering 2. Lab exercise for big data processing
 
Unit2 
Teaching Hours:15 
Machine Learning


Machine learning – Modeling Process – Training model – Validating model – predicting new observations – Supervised learning algorithms – Unsupervised learning algorithms. Introduction to deep learning – Deep Feed Forward networks – Regularization – Optimization of deep learning – Convolutional networks – Recurrent and recursive nets – applications of deep learning. Practical Assignments: 3. Lab exercise on Linear and Logistic discrimination 4. Lab exercise on K means clustering and Hierarchical clustering
 
Unit3 
Teaching Hours:15 
Introduction to Relational Database and Design


Concept and Overview of DBMS, Data Models, Database Languages, Database Administrator, Database Users, Three Schema architecture of DBMS. Basic concepts, Design Issues, Mapping Constraints, Keys, EntityRelationship Diagram, Weak Entity Sets, Functional Dependency, Different anomalies in designing a Database, Normalization: using functional dependencies, 1NF, 2NF, 3NF and BoyceCodd Normal Form Practical Assignments: 5. Lab Exercise on Database Design 6. TopDown Approach 7. Bottomup Approach
 
Unit4 
Teaching Hours:15 
Database Querying and Data Integration


SQL Basic Structure  DDL, DML, DCLIntegrity Constraints  Domain Constraints, Entity Constraints  Referential Integrity Constraints, Concept of Set operations, Joins, Aggregate Functions, Null Values, , assertions, views, Nested Subqueries – procedural extensions – stored procedures – functions cursors – Intelligent databases – ECA rule – Data Integration – ETL Process Practical Assignments: 8. Lab Exercise on SQL 9. Lab Exercise on PL/SQL 10. Lab Exercise on ETL
 
Unit5 
Teaching Hours:15 
Introduction to Data Warehouse


Data Warehousing  Defining Feature – Data warehouses and data marts –Metadata in the data warehouse – Data design and Data preparation  Dimensional Modeling  Principles of dimensional modelling – The star schema – star schema keys – Advantages of the star schema – Updates to the dimension tables – The snowflake schema – Aggregate fact tables – Families Oo Stars – MDX queries – Reporting services. Practical Assignments: 11. Lab Exercise on Analysis Services 12. Lab Exercise on Reporting Services
 
Text Books And Reference Books: 1. Davy Cielen, Arno D. B. Meysman, Mohamed Ali (2016), Introducing Data Science, Manning Publications Co. 2. Thomas Cannolly and Carolyn Begg, (2007), Database Systems, A Practical Approach to Design, Implementation and Management”, 3rd Edition, Pearson Education.
 
Essential Reading / Recommended Reading 1. Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani (2013), An Introduction to Statistical Learning: with Applications in R, Springer. 2. D J Patil, Hilary Mason, Mike Loukides, (2018), Ethics and Data Science, O’Reilly. 3. LiorRokach and OdedMaimon, (2010), Data Mining and Knowledge Discovery Handbook.
 
Evaluation Pattern CIA  50% ESE  50%
 
MST273B  SURVIVAL ANALYSIS (2021 Batch)  
Total Teaching Hours for Semester:75 
No of Lecture Hours/Week:5 
Max Marks:150 
Credits:4 
Course Objectives/Course Description 

This course will provide an introduction to the principles and methods for the analysis of timetoevent data. This type of data occurs extensively in both observational and experimental biomedical and public health studies. 

Learning Outcome 

By the end of the course, the learner will be able to: CO1: Explore the fundamental concepts of survival models CO2: Analyse survival data using various parametric models CO3: Identify NonParametric Survival techniques for applications lifetime data CO4: Demonstrate the understanding of various Competing Risks and their effects

Unit1 
Teaching Hours:15 

Basic quantities and censoring


The hazard and survival functions  Mean residual life function  competing risk  right,left and interval censoring, truncation  likelihood for censored and truncated data  Parametric and nonparametric estimation in truncated and censored cases. Practical Assignments: 1.Lab exercise on the parametric estimation of left and rightcensored data 2.Lab exercise on the parametric estimation of truncated data 3.Lab exercise on the nonparametric estimation of censored and truncated data  
Unit2 
Teaching Hours:15 

Parametric Survival Models


Parametric forms and the distribution of log time  The exponential  Weibull  Gompertz  Gamma  Generalized Gamma  CoaleMcNeil  and generalized F distributions  The U.S. life table  Approaches to modelling the effects of covariates  Parametric families  Proportional hazards models (PH)  Accelerated failure time models (AFT)  The intersection of PH and AFT. Proportional odds models (PO)  The intersection of PO and AFT  Recidivism in the U.S. Practical Assignments: 1.Lab exercise on parametric modelling pf survival data 2.Lab exercise on the proportional hazard model 3.Lab exercise on AFT models
 
Unit3 
Teaching Hours:15 

NonParametric Survival Models


Onesample estimation with censored data  The KaplanMeier estimator  Greenwood's formula  The NelsonAalen estimator  The expectation of life  Comparison of several groups: Mantel Haenszel and the logrank test. Regression: Cox's model and partial likelihood  The score and information  The problem of ties  Tests of hypotheses  Timevarying covariates  Estimating the baseline survival  Martingale residuals. Practical Assignments: 7.Lab exercise on KaplanMeier estimator and NelsonAalen estimator 8.Lab exercise on Mantel Haenszel and the logrank test 9.Lab exercise on the Cox model with timevarying covariate  
Unit4 
Teaching Hours:15 

Models for Discrete Data and Extensions


Cox's discrete logistic model and logistic regression  Modelling grouped continuous data and the complementary loglog transformation  Piecewise constant hazards and Poisson regression  Current status data versus retrospective data  Open intervals and time since the last event  Backward recurrence times  Interval censoring. Practical Assignments: 10.Lab exercise on the discrete logistic model for survival data 11.Lab exercise on Poisson regression for survival data 12.Lab exercise on Piecewise regression for survival data  
Unit5 
Teaching Hours:15 

Models for Competing Risks


Modelling multiple causes of failure  Research questions of interest  Causespecific hazards  Overall survival  Causespecific densities  Estimation: onesample and the generalized Kaplan Meier and NelsonAalen estimators  The Incidence function  Regression models  Weibull regression  Cox regression and partial likelihood  Piecewise exponential survival and multinomial logits  The identification problem  Multivariate and marginal survival  The FineGray model. Practical Assignments: 13.Lab exercise on nonparametric modelling of competing risk data 14.Lab exercise on parametric modelling of competing risk data 15.Lab exercise on multivariate survival data  
Text Books And Reference Books: 1. Klein, J. P., & Moeschberger, M. L. (2006). Survival analysis: techniques for censored and truncated data. Springer Science & Business Media. 2. Cleves, M.; W. G. Gould, and J. Marchenko (2016). An Introduction to Survival Analysis using Stata. Revised 3rd Ed. College Station, Texas: Stata Press. 3. Kalbfleisch, J. D., & Prentice, R. L. (2011). The statistical analysis of failure time data,2nd Ed. John Wiley & Sons. 4. Moore, D. F. (2016). Applied survival analysis using R. Switzerland: Springer.
 
Essential Reading / Recommended Reading 1. Singer, J.D and J. B. Willett (2003) Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence. Oxford, Oxford University Press. 2. Therneau, T. M. and P. M. Grambsch (2000). Modelling Survival Data: Extending the Cox Model, Springer, NY 3. Collett, D. (2015). Modelling survival data in medical research. Chapman and Hall/CRC.
 
Evaluation Pattern CIA  50% ESE  50%
 
MST273C  OPTIMIZATION TECHNIQUES (2021 Batch)  
Total Teaching Hours for Semester:75 
No of Lecture Hours/Week:5 

Max Marks:100 
Credits:4 

Course Objectives/Course Description 

This course is designed to train the students to develop their modelling skills in mathematics through various methods of optimization. The course helps the students to understand the theory of optimization methods and algorithms developed for solving various types of optimization problems. 

Learning Outcome 

By the end of the course, the learner will be able to:

Unit1 
Teaching Hours:15 
Linear Programming Problems (LPP)


Introduction to optimization – convex set and convex functions – simplex method: iterative nature of simplex method – additional simplex method: duality concept  dual simplex method – generalized simplex algorithm  revised simplex method: revised simplex algorithm – development of the optimality and feasibility conditions. Practical Assignments: 1. Formulate the LPP. 2. Solve the LPP using simplex method. 3. Solve the LPP using revised simplex method.  
Unit2 
Teaching Hours:15 
Integer Linear Programming


Branch and bound algorithm – cutting plane algorithm – transportation problem: northwest method, leastcost method, vogel’s approximation and method of multipliers – assignment problem: mathematical statement, Hungarian method, variations of assignment problems. Practical Assignments: 4. Solve integer LPP by cutting plane method. 5. Formulate and solve transportation problems. 6. Formulate and solve assignment problems.  
Unit3 
Teaching Hours:15 
Nonlinear Programming


Introduction – unimodal function – one dimensional optimization: Fibonacci method – golden Section Method – quadratic interpolation methods  cubic interpolation methods – direct root method: newton method and quasi newton method – Multidimensional unconstrained optimization: univariate method – Hooks and Jeeves method – Fletcher – Reeves method  Newton’s method and quasi newton’s method. Practical Assignments: 7. Solve a non LPP problem. 8. Solve an unconstrained optimization problem by a univariate method  
Unit4 
Teaching Hours:15 
Classical optimization techniques


Single variable optimization – multivariable optimization with no constraints: semidefinite case and saddle point – multivariable optimization with equality constraints: direct substitution – method of constrained variation – method of Lagrange multipliers  KuhnTucker conditions  constraint qualification – convex programming problem. Practical Assignments: 9. Solve a single variable optimization problem. 10. Solve multivariable optimization problems with equality constraints. 11. Solve a convex optimization problem.  
Unit5 
Teaching Hours:15 
Geometric and Dynamic programming


Unconstrained minimization problem – solution of an unconstrained geometric programming problem using arithmeticgeometric inequality method – primal dual relationship  constrained minimization  dynamic programming: Dynamic programming algorithm – solution of linear programming problem by dynamic programming. Practical Assignments: 12. Formulate and solve a dynamic programming problem. 13. Solve LPP through dynamic programming problems. 14. Solve a geometric programming problem.  
Text Books And Reference Books:
 
Essential Reading / Recommended Reading
 
Evaluation Pattern CIA 50% ESE50%  
MST281  RESEARCH PROBLEM IDENTIFICATION AND FORMULATION (2021 Batch)  
Total Teaching Hours for Semester:30 
No of Lecture Hours/Week:2 
Max Marks:50 
Credits:1 
Course Objectives/Course Description 

The course will be inculcating research culture which will enhance the employability skills to the students. 

Learning Outcome 

CO1: Demonstrate the objective and data collection methodology for a research problem. 
Unit1 
Teaching Hours:30 

Problem Identification


Students will do the following, 1. Identify a domain for the research project 2. Literature survey 3. Identifying the existing methodology and models 4. Writing a problem statement 5. Project presentation at the end of the process  
Text Books And Reference Books:   
Essential Reading / Recommended Reading   
Evaluation Pattern CIA  50% ESE  50%  
MST331  STATISTICAL INFERENCE II (2020 Batch)  
Total Teaching Hours for Semester:60 
No of Lecture Hours/Week:4 

Max Marks:100 
Credits:4 

Course Objectives/Course Description 



Learning Outcome 

CO1: Demonstrate the understanding of basic concepts of robust estimation and testing of hypotheses. CO2: Apply the procedures of testing hypotheses for solving reallife problems. CO3: Apply various nonparametric tests and draw conclusions to reallife problems. CO4: Develop appropriate tests for testing specific statistical hypotheses. CO5: Draw conclusions about the population with the help of various estimation and testing procedures. 
Unit1 
Teaching Hours:14 

Robust estimation


Robust estimation: The influence curve and empirical influence curve  Mestimation: Median, Trimmed and winsorized mean  Influence curve for Mestimators  Limiting distribution of Mestimators  Resampling methods: Quenouille’s Jackknife estimation, parametric and nonparametric bootstrap methods.
 
Unit2 
Teaching Hours:10 

NeymanPearson theory of testing of hypotheses


Basic concepts in statistical hypotheses testing  Simple and composite hypothesis  Critical regions  TypeI and TypeII error  Significance level  pvalue and power of a test  Randomised and nonrandomized tests  NeymanPearson lemma and its applications  Generalization of NP lemma  Construction of tests using NP lemma  Most powerful test  Uniformly most powerful test  Monotone Likelihood Ratio (MLR) property  Testing in oneparameter exponential families  Unbiased and invariant tests  Locally most powerful tests.  
Unit3 
Teaching Hours:12 

Uniformly most powerful tests


Onesided uniformly most powerful tests  Unbiased and Uniformly Most Powerful Unbiased tests for different twosided hypothesis  Extension of these results to Pitman family when only upper or lower end depends on the parameters  UMP test from αsimilar tests and αsimilar tests with Neyman structure.  
Unit4 
Teaching Hours:12 

Likelihood procedure of testing of hypotheses


Likelihood ratio test (LRT)  asymptotic properties  LRT for the parameters of binomial and normal distributions  Generalized likelihood ratio tests  ChiSquare tests  ttests  Ftests  Need for sequential tests  Sequential Probability Ratio Test (SPRT)  Wald’s fundamental identity  OC and ASN functions  Applications to Binomial, Poisson, and Normal distributions.  
Unit5 
Teaching Hours:12 

Basics of nonparametric tests


Nonparametric tests: Sign test  Chisquare tests  KolmogorovSmirnov one sample and two samples tests  Median test  Wilcoxon Signed Rank test  Mann Whitney Utest  Test for Randomness  Runs up and runs down test  Wald–Wolfowitz run test for equality of distributions  Kruskal–Wallis oneway analysis of variance  Friedman’s twoway analysis of variance  Power and asymptotic relative efficiency.  
Text Books And Reference Books:
Statistics, John Wiley and Sons.
 
Essential Reading / Recommended Reading
2nd edition. McMillan, New York.
 
Evaluation Pattern
 
MST332  MULTIVARIATE ANALYSIS (2020 Batch)  
Total Teaching Hours for Semester:60 
No of Lecture Hours/Week:4 

Max Marks:100 
Credits:4 

Course Objectives/Course Description 

The exposure provided to the multivariate data structure, multinomial and multivariate normal distribution, estimation and testing of parameters, various data reduction methods would help the students in having a better understanding of research data, its presentation and analysis. This course helps to understand multivariate data analysis methods and their applications in various research areas. 

Learning Outcome 

By the end of the course, the learner will be able to: CO1: Describe concepts of multivariate normal distribution. CO2: Demonstrate the concepts of MANOVA and MANCOVA. CO3: Identify various classification methods for multivariate data. CO4: Analyze various data reduction methods for the multivariate data structure. CO5: Interpret the results of various multivariate methods.

Unit1 
Teaching Hours:12 

: Multivariate Distributions


Basic concepts on multivariate variables  Multivariate normal distribution  Marginal and conditional distribution  Concept of random vector  Its expectation and Variance  Covariance matrix. Marginal and joint distributions  Conditional distributions and Independence of random vectors  Multinomial distribution  Characteristic functions in higher dimensions  Multiple regressions and multiple correlations Partial regression and Partial correlation (illustrative examples).  
Unit2 
Teaching Hours:12 

MANOVA and MANCOVA


Multivariate analysis of variance (MANOVA) and Covariance (MANCOVA) of one and twoway classified data with their interactions  Univariate and Multivariate TwoWay Fixedeffects Model with Interaction.  
Unit3 
Teaching Hours:12 

Equality of Mean and Variance Vector


Wishart distribution (definition, properties) Construction of tests Union  Intersection and likelihood ratio principles  Inference on mean vector  Hotelling's T^{2} Comparing Mean Vectors from Two Populations  Bartlett’s Test.  
Unit4 
Teaching Hours:12 

Classification and Discriminant Procedures


Concepts of discriminant analysis  Computation of linear discriminant function (LDF)  Classification between k multivariate normal populations based on LDF  Fisher’s Method for discriminating two or several populations  Evaluating Classification Functions  Probabilities of misclassification and their estimation  Mahalanobis D2.  
Unit5 
Teaching Hours:12 

Factor Analysis and Cluster Analysis


Factor analysis:  Orthogonal factor model Factor loadings Estimation of factor loadings Factor scores and Its applications. Cluster Analysis:  Distances and similarity measures  Hierarchical clustering methods  K Means method.  
Text Books And Reference Books: 1. Anderson, T.W. (2004). An Introduction to Multivariate Statistical Analysis. John Wiley. New York. 2. Johnson, R.A. and Wichern, D.W. (2018). Applied Multivariate Statistical Analysis. 6th edn. PrenticeHall. London.
 
Essential Reading / Recommended Reading 1. Rohatgi, V.K. and Saleh, A.K.M.E. (2015). An Introduction to Probability Theory and Mathematical Statistics. 2nd edn. John Wiley & Sons. New York. 2. Srivastava, M.S. and Khatri, C.G. (1979). An Introduction to Multivariate Statistics. NorthHolland. 3. Muirhead, R.J. (1982). Aspects of Multivariate Statistical Theory. John Wiley. New York.
 
Evaluation Pattern
 
MST371  TIME SERIES ANALYSIS (2020 Batch)  
Total Teaching Hours for Semester:90 
No of Lecture Hours/Week:6 

Max Marks:150 
Credits:5 

Course Objectives/Course Description 

The course considers statistical techniques to evaluate processes occurring through time. It introduces students to time series methods and the applications of these methods to different types of data in various fields. Time series modeling techniques including AR, MA, ARMA, ARIMA, and SARIMA will be considered with reference to their use in forecasting. The objective of this course is to equip students with various forecasting techniques and to familiarize themselves with modern statistical methods for analyzing timeseries data. 

Learning Outcome 

CO1: Demonstrate the understanding of basic concepts of analyzing time series, including white noise, trend, seasonality, cyclical component, autocovariance and autocorrelation function. CO2: Apply the concept of stationarity to the analysis of timeseries data in various contexts. CO3: Select the appropriate model, to fit parameter values, examine residual analysis, and to carry out the forecasting calculation. CO4: Apply various techniques of seasonal time series models, including the seasonal autoregressive integrated moving average (SARIMA) models and Winters exponential smoothing. CO5: Demonstrate the principles behind modern forecasting techniques, which includes obtaining the relevant data and carrying out the necessary computation using R software.

Unit1 
Teaching Hours:20 
Basic concepts in time series analysis


Stochastic Process  Time series as a discrete parameter stochastic process  Auto – Covariance  Autocorrelation and their properties  Exploratory time series analysis graphical analysis  classical decomposition model  concepts of trend, seasonality and cycle  Estimation of trend and seasonal componentsElimination of trend and seasonality  Method of differencing  Moving average smoothing  Method of seasonal differencing Practical Assignments: 1.Graphical representation of time series, plots of ACF and PACF and their interpretation 2.Examples of trend, seasonal and cyclical time series and estimation of trend and seasonal components 3. Exercise on Moving average smoothing to eliminate trend and illustration on the method of differencing to eliminate trend and seasonality. 4.Exercise on leastsquare fitting to estimate and eliminate the trend component.  
Unit2 
Teaching Hours:20 
Stationary time series models


Stationary time series models  Concepts of weak and strong stationarity  General linear Process  AutoRegressive(AR), Moving Average(MA), and AutoRegressive Moving Average (ARMA) processes – their properties  conditions for stationarity and invertibility model identification based on ACF and PACF Maximum likelihood estimation  Yule Walker Estimation  order selection ( AIC and BIC )  Residual Analysis  Box Jenkins methodology to the identification of stationary time series models Practical Assignments: 5.Exercise on fitting AR model 6. Exercise on fitting MA model 7. Exercise on fitting ARMA model 8.Modelidentification using ACF and PACF, Model selection using AIC and BIC 9. Residual analysis and diagnosis check for AR, MA, and ARMA models
 
Unit3 
Teaching Hours:15 
Nonstationary time series models


Concept of nonstationarity  Spurious trends and regressionsunit root tests: DickeyFuller (DF) test  Augmented DickeyFuller(ADF) test – AutoRegressive Integrated Moving Average(ARIMA(p,d,q)) models  Difference equation form of ARIMA Random shock form of ARIMA  An inverted form of ARIMA Practical Assignments: 10. Exercise on the identification of nonstationary series from various plots. 11. Exercise on testing nonstationarity using ADF test, Exercise on fitting ARIMA models. 12. Residual analysis and diagnosis check for the ARIMA model.  
Unit4 
Teaching Hours:15 
Seasonal time series models


Analysis of seasonal models  parsimonious models for seasonal time series  Seasonal unit root test (HEGY test)  General multiplicative seasonal models  Seasonal ARIMA models  estimation  Residual analysis for seasonal time series.
Practical Assignments: 13. Exercise on the identification of additive and Multiplicative time series 14.Exercise on testing the presence of seasonality and on fitting Seasonal ARIMA models 15. Residual analysis and diagnosis check for Seasonal ARIMA model  
Unit5 
Teaching Hours:20 
Forecasting Techniques


In sample and out of sample forecast  Simple exponential and moving average smoothing  Holt Exponential Smoothing  Winter exponential smoothing  Forecasting trend and seasonality in Box Jenkins model: Method of minimum mean squared error(MMSE) forecast  their properties  forecast error Practical Assignments: 16.Exercise on Simple exponential smoothing and Holt Exponential Smoothing 17.Exercise on Winters exponential smoothing. 18.Exercise on forecasting using ARIMA models. 19.Exercise on forecasting using seasonal ARIMA models.  
Text Books And Reference Books: 1. Box, G. E., Jenkins, G. M., Reinsel, G. C., & Ljung, G. M. (2015). Time series analysis: forecasting and control. John Wiley & Sons. 2. Chatfield, C., & Xing, H. (2019). The analysis of time series: an introduction with R. CRC Press.  
Essential Reading / Recommended Reading 1. Hamilton, J. D. (2020). Time series analysis. Princeton university press. 2. Brockwell, P. J., & Davis, R. A. (2016). Introduction to time series and forecasting. springer.
 
Evaluation Pattern CIA  50% ESE  50%  
MST372A  STATISTICAL MACHINE LEARNING (2020 Batch)  
Total Teaching Hours for Semester:75 
No of Lecture Hours/Week:5 
Max Marks:150 
Credits:4 
Course Objectives/Course Description 

Machine learning has a wide array of applications that belongs to different fields, such as biomedical research, reliability of large structures, space research, digital marketing, etc. This course will equip students with a wide variety of models and algorithms for machine learning and prepare students for research or industry application of machine learning techniques. 

Learning Outcome 

By the end of the course, the learner will be able to:
CO1: Demonstrate the understanding of basic concepts of statistical machine learning. CO2: Apply classification algorithms for qualitative data. CO3: Analyse high dimensional data using principal component regression learning algorithms. CO4: Construct classification and regression trees by random forests. CO5: Create a statistical learning model using support vector machines

Unit1 
Teaching Hours:15 
Statistical learning


Statistical learning: definitionprediction accuracy and model interpretabilitysupervised and unsupervised learningassessing model accuracy important problems in data mining: classification, regression, clustering, ranking, density estimation Concepts: training and testing, crossvalidation, overfitting, bias/variance tradeoff, regularized learning equation simple and multiple linear regression algorithms.
Practical Assignments:
1. Lab exercise on data preparation and using simple linear regression
2. Lab exercise on model assessment simple linear regression
3. Lab exercise on data preparation with multiple linear regression
 
Unit2 
Teaching Hours:15 
Classification algorithms


Logistic model training and testing the modellinear discriminant analysisquadratic discriminant analysis Use of Bayes’ theoremk nearest neighbours  Naive Bayes’ Adaboost.
Practical Assignments:
4. Lab exercise on the logistic model
5. Lab exercise on discriminant analysis
6. Lab exercise on Naïve Bayes’ and kNN classifiers
 
Unit3 
Teaching Hours:15 
Linear model selection and regularization


Optimal modelshrinkage methods: ridge and lasso regressionDimension reduction methods: principal component (PC) regression and partial least square (PLS) regression: Nonlinear models: regression splinespolynomial – Generalized additive models
Practical Assignments: 7. Lab exercise on ridge regression 8. Lab exercise on Lasso regression 9. Lab exercise on PC regression 10. Lab exercise on PLS regression
 
Unit4 
Teaching Hours:15 
Treebased methods


Decision treeregression trees  bagging  random forests  boosting  classification treesboostingtree vs linear models.
Practical Assignments: 11. Lab exercise on decision trees 12. Lab exercise on regression trees 13. Lab exercise on random forests 14. Lab exercise on classification trees  
Unit5 
Teaching Hours:15 
Support vector machines and resampling procedures


Maximal classifiersupport vector classifierssupport  rank boost (ranking algorithm)  hierarchical Bayesian modelling for density  resampling techniquesbootstrap clustering algorithms: Kmeans algorithm.
Practical Assignments: 15. Lab exercise on SVM classifier 16. Lab exercise on rank boost algorithm 17. Lab exercise on kernel density estimation 18. Lab exercise on kmeans clustering  
Text Books And Reference Books:
 
Essential Reading / Recommended Reading
 
Evaluation Pattern CIA  50% ESE  50%  
MST372B  BIOSTATISTICS (2020 Batch)  
Total Teaching Hours for Semester:75 
No of Lecture Hours/Week:5 
Max Marks:150 
Credits:4 
Course Objectives/Course Description 

This course provides an understanding of various statistical methods in describing and analyzing biological data. Students will be equipped with an idea about the applications of statistical hypothesis testing, related concepts and interpretation in biological data. 

Learning Outcome 

By the end of the course, the learner will be able to:
CO1: Demonstrate the understanding of basic concepts of biostatistics and the process involved in the scientific method of research. CO2: Identify how the data can be appropriately organized and displayed. CO3: Interpret the measures of central tendency and measures of dispersion. CO4: Interpret the data based on the discrete and continuous probability distributions. CO5: Apply parametric and nonparametric methods of statistical data analysis. 
Unit1 
Teaching Hours:15 

Introduction to Biostatistics


Presentation of data  graphical and numerical representations of data  Types of variables, measures of location  dispersion and correlation  inferential statistics  probability and distributions  Binomial, Poisson, Negative Binomial, Hyper geometric and normal distribution.
Practical Assignments:
 
Unit2 
Teaching Hours:15 

Parametric and Non  Parametric methods


Parametric methods  one sample ttest  independent sample ttest  paired sample ttest  oneway analysis of variance  twoway analysis of variance  analysis of covariance  repeated measures of analysis of variance  Pearson correlation coefficient  Nonparametric methods: Chisquare test of independence and goodness of fit  Mann Whitney U test  Wilcoxon signedrank test  Kruskal Wallis test  Friedman’s test  Spearman’s correlation test.
Practical Assignments:
 
Unit3 
Teaching Hours:15 

Generalized linear models


Review of simple and multiple linear regression  introduction to generalized linear models  parameter estimation of generalized linear models  models with different link functions  binary (logistic) regression  estimation and model fitting  Poisson regression for count data  mixed effect models and hierarchical models with practical examples. Practical Assignments:
 
Unit4 
Teaching Hours:15 

Epidemiology


Introduction to epidemiology, measures of epidemiology, observational study designs: case report, case series correlational studies, crosssectional studies, retrospective and prospective studies, analytical epidemiological studiescase control study and cohort study, odds ratio, relative risk, the bias in epidemiological studies.
Practical Assignments:
 
Unit5 
Teaching Hours:15 

Demography


Introduction to demography, mortality and life tables, infant mortality rate, standardized death rates, life tables, fertility, crude and specific rates, migrationdefinition and concepts population growth, measurement of population growtharithmetic, geometric and exponential, population projection and estimation, different methods of population projection, logistic curve, urban population growth, components of urban population growth.
Practical Assignments:
 
Text Books And Reference Books:
 
Essential Reading / Recommended Reading
 
Evaluation Pattern 50% Continuous Internal Asssessssment (CIA). 50% End Semester Examination.  
MST372C  RELIABILITY ENGINEERING (2020 Batch)  
Total Teaching Hours for Semester:75 
No of Lecture Hours/Week:5 

Max Marks:150 
Credits:4 

Course Objectives/Course Description 

This course will provide knowledge in different probability models in the reliability evaluation of the system and its components. Reliability engineering is applied in the industry to reduce failures, ensure effective maintenance and optimize repair time. 

Learning Outcome 

By the end of the course, the learner will be able to: CO1: Demonstrate the understanding of basic concepts of reliability. CO2: Analyse system reliability using probability models. CO3: Evaluate reliability from the lifetime data using common estimation procedures CO4: Create a stressstrength model for system reliability. 
Unit1 
Teaching Hours:15 
Basic concepts


Reliability of a system  failure rate  mean, variance and percentile residual life: identities connecting them  notions of ageing  IFR, IFRA, NBU, NBUE, DMRL, HNBUE, NBUC, etc. and their mutual implications  TTT transforms and characterization of ageing classes.
Practical Assignments:
 
Unit2 
Teaching Hours:15 
Lifetime models


Nonmonotonic failure rates and mean residual life functions  study of lifetime models: exponential, Weibull, lognormal, generalized Pareto, gamma with reference to basic concepts and ageing characteristics  bathtub and upsidedown bathtub failure rate distributions
Practical Assignments: 3. Exercise on exponential lifetime model 4. Exercise on Weibull lifetime model 5. Exercise on bathtub shaped lifetime model  
Unit3 
Teaching Hours:15 
System reliability


Reliability systems with dependents components: Parallel and series systems, k out of n Systems  ageing properties with dependent and independents components  concepts and measures of dependence on reliability  RCSI, LCSD, PF2, WPQD. Practical Assignments: 6. Exercise on reliability evaluation of series system 7. Exercise on reliability evaluation of a parallel system 8. Exercise on reliability evaluation of k out of n system 9. Exercise on reliability evaluation of dependent component system
 
Unit4 
Teaching Hours:15 
Reliability estimation


Reliability estimation using MLE: exponential, Weibull and gamma distributions based on censored and noncensored samples  UMVU estimation of reliability function  Bayesian reliability estimation of exponential and Weibull models Practical Assignments: 10. Exercise on ML estimation under noncensored samples. 11. Exercise on ML estimation under censored samples. 12. Exercise on Bayesian estimation of reliability.  
Unit5 
Teaching Hours:15 
Life testing


Life testing: basics – modelling lifetime – Accelerated Life Time (ALT) models cumulative exposure models (CEM)  exponential CEM – stressstrength reliability – exponential stressstrength model. Practical Assignments: 13. Exercise on basic life testing procedure. 14. Exercise on exponential CEM model. 15. Exercise on stressstrength reliability.  
Text Books And Reference Books: 1. Birolini, A. (2013). Reliability engineering: theory and practice. Springer Science & Business Media.. 2. Bain, L. (2017). Statistical analysis of reliability and lifetesting models: theory and methods. Routledge.  
Essential Reading / Recommended Reading
 
Evaluation Pattern CIA  50% ESE  50%  
MST373A  NUMERICAL ANALYSIS (2020 Batch)  
Total Teaching Hours for Semester:75 
No of Lecture Hours/Week:5 
Max Marks:150 
Credits:4 
Course Objectives/Course Description 

This course deals with the theory and application of different numerical methods techniques to solve the complex problems that arise in the modern world of science. The course highlights that through the numerical algorithms, it is definite to arrive at a solution which is efficient and stable for large scale systems. 

Learning Outcome 

By the end of the course, the learner will be able to: CO1: Demonstrate the understanding of floatingpoint numbers and the role of errors and their analysis in numerical methods. CO2: Identity accuracy, consistency, stability and convergence of numerical methods. CO3:Derive numerical solution of the algebraic and transcendental equations, ordinary differential equations and boundary value problems. CO4: Interpret, analyse and evaluate results from numerical computations. 
Unit1 
Teaching Hours:15 
Error analysis and basics of the solution of algebraic equations


Errors and their analysis – Floating Point representation of numbers – Solution of algebraic and Transcendental equations: Bisection method, fixedpoint iteration method, the method of False position, Newton Raphson method and Muller’s method. The solution of linear systems – Matrix inversion method – Gauss elimination method – GaussSeidel and GaussJacobi iterative methods. Practical Assignments: 1. Solutions to algebraic equations using Bisection and fixed point methods 2. Solutions to algebraic and transcendental equations using Newton Raphson and Muller’s method. 3. Solving system of linear equations using Matrix inversion and Gauss elimination methods 4. Finding real roots to a system of linear equations using GaussSeidel and GaussJacobi iterative methods.
 
Unit2 
Teaching Hours:15 
Advanced methods to Solve algebraic and transcendental equations


Convergence criterion, Aitken’sprocess  Sturm sequence method to identify the number of real roots, Bairstow’s method  Graeffe’s root squaring method  BirgeVieta method  Solution of Linear system of algebraic equations: LUdecomposition methods (Crout’s, Cholesky and Delittle methods), consistency and illconditioned system of equations, Tridiagonal system of equations, Thomas algorithm.
Practical Assignments:
5. Identifying real roots for algebraic equations using the Sturm sequence method and Bairstow’s method.
6. Solving equations using the BirgeVieta method.
7. Solving system of linear equations using LU decomposition methods.
8. Examining consistency of the system of equations using Tridiagonal system of equations and Thomas algorithm.
 
Unit3 
Teaching Hours:15 
Finite Differences and Interpolation


Finite difference: Forward difference, Backward difference and Shift operators – Separation of symbols – Newton’s Formula for interpolation – Lagrange’s interpolation formulae – Numerical differentiation – Numerical integration: Trapezoidal rule, Simpson’s onethird rule and Simpson’s threeeight rule. Numerical ODE: Taylor’s series – Picard’s method – Euler’s method – Modified Euler’s method – Runge Kutta Method. Practical Assignments: 9. Exercise on Newton’s and Lagrange's interpolation formulae 10. Integration using Trapezoidal rule and Simpon’s rules. 11. Numerical Solutions for ODE using Taylor’s series and Picard’s Method
12. Numerical Solutions for ODE using Euler’s method, Modified Euler’s method and Runge Kutta Method.
 
Unit4 
Teaching Hours:15 
Advanced Numerical Integration


Lagrange, Hermite, Cubicspline’s method – with uniqueness and error term, polynomial interpolation: Chebychev and Rational function approximation, Gaussian quadrature, GaussLegendre, GaussChebychev formulas.
Practical Assignments:
13. Integration using Hermite and Cubicspline’s method
14. Interpolation for polynomial equations Chebychev and rational function approximation
15. Interpolation for polynomial equations Gaussian quadrature and GaussLegender
16. Numerical integration through GaussChebyshev formulas.
 
Unit5 
Teaching Hours:15 
Advanced numerical solutions of Ordinary Differential equations


Initial value problems – Multistep method – AdamsMoulton method – Stability (convergence and truncation error) – Boundary value problems: second order finite difference method – first, second and third types by shooting method – RayleighRitz method – Galerkin method. Practical Assignments: 17. Solution for initial value problems using Multistep and AdamsMoulton method 18. Solving ODE using shooting, RayleighRitz and Galerkin methods  
Text Books And Reference Books:
 
Essential Reading / Recommended Reading 1. R.L. Burden and J. Douglas Faires, Numerical Analysis, 9^{th} Edition, Boston: Cengage Learning, 2011. 2. S.C. Chopra and P.C. Raymond, Numerical Methods for Engineers, New Delhi: Tata McGrawHill, 2010. 3. Graham. W Griffiths, Numerical Analysis using R solution to ODEs and PDEs, Cambridge University Press, 2016. 4. Jaan Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University Press, 2013.  
Evaluation Pattern CIA  50% ESE 50%  
MST373B  NONPARAMETRIC METHODS (2020 Batch)  
Total Teaching Hours for Semester:75 
No of Lecture Hours/Week:5 
Max Marks:150 
Credits:4 
Course Objectives/Course Description 

This course will provide the basic theory and computing tools to perform nonparametric tests, including the Sign test, Wilcoxon signedrank test, Median test etc. KruskalWallis for oneway and multiple comparisons, linear rank test for location and scale parameters and measure of association in bivariate populations are other nonparametric tests covered in this course. The aim of the course is the indepth presentation and analysis of the most common methods and techniques of nonparametric statistics such as sign test, rank test, run test, median test etc. 

Learning Outcome 

By the end of the course, the learner will be able to: CO1: Compare different nonparametric hypothesis tests in twosample problems. CO2: Construct interval estimators for population medians and other population parameters based on rankbased methods. CO3: Formulate, test and interpret various hypothesis tests for location, scale, and independence problems CO4: Demonstrate different measures of association for bivariate samples. 
Unit1 
Teaching Hours:15 
OneSample and PairedSample Procedures


The quantile function  the empirical distribution function  statistical properties of order statistics confidence interval for a population quantile hypothesis testing for a population quantile the sign test and confidence interval for the median  rankorder statistics treatment of ties in rank tests Wilcoxon signedrank test and confidence interval
Practical Assignments:
 
Unit2 
Teaching Hours:15 
The General twosample problem


WaldWolfowitz runs test  KolmogorovSmirnov twosample test  median test  the control median test  the MannWhitney U test
Practical Assignments: 5.Exercise on WaldWolfowitz runs test 6.Exercise on KolmogorovSmirnov twosample test. 7.Exercise on Median test and control median test.
8.Exercise on MannWhitney U test.
 
Unit3 
Teaching Hours:15 
Linear Rank Tests for the Location and Scale Problem


Definition of linear rank statistics  Wilcoxon ranksum test  mood test  FreundAnsariBradleyDavidBarton tests  SiegelTukey test
Practical Assignments: 9.Exercise on Wilcoxon ranksum test and mood test 10.Exercise on FreundAnsariBradleyDavidBarton tests. 11. Exercise on SiegelTukey test
 
Unit4 
Teaching Hours:15 
Tests of the Equality of k Independent Samples


extension of the median test  the extension of the control median test  the KruskalWallis oneway ANOVA test and multiple comparisons  tests against ordered alternatives  comparisons with a control  ChiSquare test for k proportions
Practical Assignments: 12.Exercise on the extension of the median test and control median test. 13.Exercise on KruskalWallis oneway ANOVA test. 14.Exercise on chisquare test for k proportions
 
Unit5 
Teaching Hours:15 
Measures of Association for Bivariate Samples


Introduction: definition of measures of association in a bivariate population  Kendall’s Tau coefficient  Spearman’s coefficient of rank correlation  relations between R and T; E(R), t, and r
Practical Assignments: 15.Exercise on Kendall’s Tau coefficient. 16.Exercise on Spearman’s coefficient of rank correlation
 
Text Books And Reference Books:
 
Essential Reading / Recommended Reading
 
Evaluation Pattern CIA 50% ESE 50%  
MST373C  THEORY OF GAMES AND STATISTICAL DECISIONS (2020 Batch)  
Total Teaching Hours for Semester:75 
No of Lecture Hours/Week:5 
Max Marks:150 
Credits:4 
Course Objectives/Course Description 

Game theory and the decision is a branch of Mathematics and Statistics that enables to study of the strategic interactions amongst rational decisionmakers. Traditionally, gametheoretic tools have been applied to solve problems in Economics, Business, Political Science, Biology, Sociology, Computer Science, Logic, and Ethics. In recent years, applications of game theory have been successfully extended to several areas of engineered / networked system such as wireline and wireless communications, static and dynamic spectrum auction, social and economic networks. 

Learning Outcome 

CO1: Demonstrate the basics of a “game” and translate the basics of a “game” into a wide range of conflicts. CO2: Apply the minimax, randomized, and nonrandomized decision rules to reallife problems. CO3: Infer the importance of rules based on sufficient and essentially complete class. CO4: Identify the invariant statistical decision problems and their solutions CO5: Apply the Bayes rules in multiple decision problems and to address Slippage problems. 
Unit1 
Teaching Hours:15 
Game and Decision Theories


Theory of games  zerosum game  minimax  maxmin  dominance strategy  the value of the game  Basic elements of game and Decision  Comparison of the two theories  Decision function and Risk function; Randomization and optimal decision rules  Form of Bayes rules for estimation. Practical Assignments:
 
Unit2 
Teaching Hours:15 
Main Theorems of Decision Theory


Admissibility and completeness  Fundamental theorems of Game and Decision theories  Admissibility of Bayes rules  Existence of Bayes decision rules  Existence of minimal complete class  Essential completeness of the class of nonrandomized decision rules  Minimax theorem  The complete class theorem  Methods for finding minimax rules.
Practical Assignments:
 
Unit3 
Teaching Hours:15 
Sufficient Statistics


Sufficient Statistics and essentially complete class of rules based on Sufficient Statistics  Complete Sufficient Statistics  Continuity of the risk function. Practical Assignments:
 
Unit4 
Teaching Hours:15 
Invariant Statistical Decision Problems


Invariant decision problems and rules  Admissible and minimax invariant rules  Minimax estimates of location parameter  Minimax estimates for the parameters of normal distribution. Practical Assignments:
 
Unit5 
Teaching Hours:15 
Multiple Decision problems


Monotone Multiple decision problems  Bayes rules in multiple decision problems  Slippage problems. Practical Assignments:
 
Text Books And Reference Books:
.  
Essential Reading / Recommended Reading
 
Evaluation Pattern CIA  50% ESE  50%  
MST381  RESEARCH MODELING AND IMPLEMENTATION (2020 Batch)  
Total Teaching Hours for Semester:120 
No of Lecture Hours/Week:8 
Max Marks:200 
Credits:4 
Course Objectives/Course Description 

This will equip the student to apply statistical methods they have studied in various courses and present their work through research articles. 

Learning Outcome 

By the end of the course, the learner will be able to CO1: Apply statistical techniques to a reallife problem. CO3: Interpret and conclude the statistical analysis scientifically. CO4: Present the work done through presentation and research article. 
Unit1 
Teaching Hours:120 
Modelling and Implementation


1. Apply various statistical methods in solving a reallife problem. 2. Comparison with the existing models or results. 3. Writing research article 4. Presentation of the article  
Text Books And Reference Books: _  
Essential Reading / Recommended Reading _  
Evaluation Pattern CIA 50% ESE 50%  
MST431  ADVANCED OPERATIONS RESEARCH (2020 Batch)  
Total Teaching Hours for Semester:60 
No of Lecture Hours/Week:4 
Max Marks:100 
Credits:4 
Course Objectives/Course Description 

Operations research helps in solving problems in different environments that need decisions. The module includes the topics : linear programming, integer programming, nonlinear programming, simple queueing models and inventory models. The aim of the course is to provide the students, how to formulate the problems into mathematical models and to use the appropriate methods to solve them. 

Learning Outcome 

By the end of the course, the learner will be able to: CO1:Understand mathematical models used in Operations Research and to use solution methods such as Simplex, revised simplex and dual simplex for solving linear programming problems. CO2: Solve integer programming models using Cutting plane and brand and bound methods. CO3: Solve nonlinear programming problems with equality and inequality constraints. CO4: Analyse serviceoriented problems usingqueuing models. CO5: Understand the methods used by organizations to obtain the right quantities of stock or inventory, as well as familiarize themselves with inventory management practices. 
Unit1 
Teaching Hours:12 

Linear Programming problem (LPP)


General Linear programming problem  Formulation  Solution through graphical, Simplex, BigM and Two phase methods  Revised Simplex method  BigM and Two phase Revised Simplex methods  Duality  Primaldual relationships  Dual Simplex method.
 
Unit2 
Teaching Hours:12 

Integer Programming


Gomory’s AllInteger CuttingPlane Method  Construction of Gomory’s Constraint  Gomory’s MixedInteger CuttingPlane Method  Construction of Additional Constraint for MixedInteger Programming Problem  Branch and Bound Method.  
Unit3 
Teaching Hours:12 

Nonlinear programming problem (NLPP)


General nonlinear programming problem  Constrained optimization with equality constraints  Necessary conditions for a generalized NLPP (without proof)  Sufficient conditions for a general NLPP with one constraint (without proof)  Sufficient conditions for a general problem with m(<n) constraints (without proof) Constrained optimization with inequality constraints  KuhnTucker conditions for general NLPP with m(<n) constraints (without proof). Constrained optimization with inequality constraints  KuhnTucker conditions for general NLPP with m(<n) constraints (without proof)  
Unit4 
Teaching Hours:12 

Queueing Theory


Basics of queuing model  Probability distribution in a queueing system  Distribution of arrivals (Pure birth model)  Distribution of departures (Pure death model)  Poisson queuing model: (M/M/1) : (GD/∞/∞)  (M/M/1) : (N/FCFS/∞)  (M/M/c) : (∞/FCFS/∞)  (M/M/c) : (N/FCFS/∞).  
Unit5 
Teaching Hours:12 

Inventory Models


Deterministic inventory Models  Economic Order Quantity(EOQ) models  Classic EOQ models  Problems with no shortages  The fundamental EOQ Problems: EOQ problems with several production runs of unequal length  Problems with price breaks  One price break  More than one price break  Probabilistic inventory models  Single Period Problem without setup cost  I.  
Text Books And Reference Books: 1. Bhunia, A. K., Sahoo, L., & Shaikh, A. A. (2019). Advanced Optimization and Operations Research. Springer.
 
Essential Reading / Recommended Reading 1. Srinivasan, G. (2017). Operations Research: principles and applications. PHI Learning Pvt. Ltd. 2. Taha, H. A. (2013). Operations research: an introduction. Pearson Education India. 3. Shortle, J. F., Thompson, J. M., Gross, D., & Harris, C. M. (2018). Fundamentals of queueing theory (Vol. 399). John Wiley & Sons. 4. Sharma, J. K. (2016). Operations research: theory and applications. Trinity Press, an imprint of Laxmi Publications Pvt. Limited.
 
Evaluation Pattern
 
MST432  DESIGN AND ANALYSIS OF EXPERIMENTS (2020 Batch)  
Total Teaching Hours for Semester:60 
No of Lecture Hours/Week:4 

Max Marks:100 
Credits:4 

Course Objectives/Course Description 

This course will provide students with a mathematical background of various basic designs involving oneway and twoway elimination of heterogeneity and characterization properties. To prepare the students in deriving the expressions for analysis of experimental data and selection of appropriate designs in planning a scientific experimentation 

Learning Outcome 

CO1: Demonstrate basic principles and characterization properties of various designs of the experiment.CO2: Identify appropriate design of experiments to solve research problems of various domains.CO3: Design factorial experiments with confounding.CO4: Construct split and strip plot designs. CO5: Analyse the Incomplete Block designs.

Unit1 
Teaching Hours:12 

Basic of design of experiments


Basic principles of design of experiments  Randomization  Replication and Local control  Uniformity trials  Size and Shape of plots and blocks  Elements of linear estimation  Analysis of variance  Completely Randomized Design (CRD)  Randomized Complete Block Design (RCBD) and Latin Square Design (LSD)  Missing plot techniques  
Unit2 
Teaching Hours:12 

Analysis of Covariance


Analysis of covariance  Ancillary/Concomitant variable and study variable  Linear model for ANCOVA  Adjustment of treatment sum of squares in ANCOVA  One  Way and twoway classification with a single concomitant variable in CRD and RCBD designs.  
Unit3 
Teaching Hours:12 

Factorial experiments


Factorial experiments  Simple experiment (single factor) vs Factorial experiments  Mixed and Fixed factor experiments  Treatment combination in a factorial experiment  Simple effect  Main effect and Interaction effect in a factorial experiment  Yates method of computing factorial effects totals  Complete and partial confounding in symmetrical factorial experiments (2^{2}, 2^{3}, 3^{3}, 2^{n}and 3^{n} series)  Gain in the factorial experiments.  
Unit4 
Teaching Hours:12 

Split  Plot and Strip  Plot designs


Split  Plot, Split  Split plot and Strip  Plot (Split Block) design  Situation for the usage of the design  Layout and analysis of the designs  Difference in the error components in the designs  Selection of factor for allocation in plots (main/sub)  Combined experiments  Cross  Over designs  
Unit5 
Teaching Hours:12 

Incomplete Block Designs


Balanced Incomplete Block (BIB) designs  General properties and Analysis with and without recovery of information  Construction of BIB designs  Parameter relationship  Intra and interblock Analysis  Partially Balanced Incomplete Block Design (PBIBD)  Youden square designs  Lattice designs  
Text Books And Reference Books:
 
Essential Reading / Recommended Reading
 
Evaluation Pattern
 
MST433  STATISTICAL QUALITY CONTROL (2020 Batch)  
Total Teaching Hours for Semester:60 
No of Lecture Hours/Week:4 

Max Marks:100 
Credits:4 

Course Objectives/Course Description 

This course provides an introduction to the application of statistical tools in the industrial environment to study, analyze and control the quality of products


Learning Outcome 

By the end of the course, the learner will be able to: CO1: Understand concepts of control charts in quality improvement CO2: Analyse process capability using control charts CO3: Construct modified control charts to monitor the process CO4: Evaluate the quality of products using various acceptance sampling plans 
Unit1 
Teaching Hours:12 

Statistical Process Control


Meaning and scope of statistical quality control  Causes of quality variation  Control charts for variables and attributes  Rational subgroups  Construction and operation of, σ, R, np, p, c and u charts  Operating characteristic curves of control charts. Process capability analysis using histogram, probability plotting and control chart  Process capability ratios and their interpretations.
 
Unit2 
Teaching Hours:12 

Advanced Control Charts


Specification limits and tolerance limits  Modified control charts  Basic principles and design of cumulative  sum control charts – Concept of Vmask procedure – Tabular CUSUM charts  Construction of Moving range  movingaverage and geometric movingaverage control charts.  
Unit3 
Teaching Hours:12 

Attribute sampling plans


Acceptance sampling: Sampling inspection by attributes – single, double and multiple sampling plans – Rectifying Inspection  Measures of performance: OC, ASN, ATI and AOQ functions  Concepts of AQL, LTPD and IQL  Dodge – Romig and MILSTD105D tables
 
Unit4 
Teaching Hours:12 

Variables Sampling Plans


Sampling inspection by variables  known and unknown sigma variables sampling plan  Merits and limitations of variables sampling plan  single, double and multiple sampling plans  Derivation of OC curve – determination of plan parameters.  
Unit5 
Teaching Hours:12 

Continuous and Cumulative Sampling Plans


Continuous Sampling Plans (CSP): CSP1 CSP2  CSP3  SkipLot Sampling Plans (SkSP): SkSP1  SkSP2 with SSP as reference plan  Chain Sampling Plans (ChSP  1) with SSP as reference plan  TightenNormalTighted (TNT) sampling plan with SSP as reference plan– Decision Lines.  
Text Books And Reference Books: 1. Montgomery, D. C. (2019). Introduction to Statistical Quality Control, Eighth Edition, Wiley India, New Delhi.  
Essential Reading / Recommended Reading 1 Juran, J.M., and De Feo, J.A. (2010). Juran’s Quality control Handbook – The Complete Guide to Performance Excellence, Sixth Edition, Tata McGrawHill, New Delhi. 2. Schilling, E. G., and Nuebauer, D.V. (2009). Acceptance Sampling in Quality Control, Second Edition, CRC Press, New York 3. Duncan, A. J. (2003.). Quality Control and Industrial Statistics, IrwinIllinois, US.  
Evaluation Pattern
 
MST471A  NEURAL NETWORKS AND DEEP LEARNING (2020 Batch)  
Total Teaching Hours for Semester:75 
No of Lecture Hours/Week:5 

Max Marks:150 
Credits:4 

Course Objectives/Course Description 

The objective of this course is to provide fundamental knowledge of neural networks and deep learning. This course gives a brief idea of the basics of neural networks, shallow and deep neural networks and other methods to build various research projects. 

Learning Outcome 

By the end of the course, the learner will be able to: CO1: Identify the difference between biological and arithmetic neural networks. CO2: Demonstrate the different types of supervised learning algorithms. CO3: Build and train various Convolution Neural Networks CO4: Implement Recurrent Neural Networks and other artificial neural networks for realtime applications. 
Unit1 
Teaching Hours:15 
Introduction to Artificial Neural Networks


Fundamental concepts of Artificial Neural Networks (ANN)  Biological neural networks  Comparison between biological neuron and artificial neuron  Evolution of neural networks  Scope and limitations of ANN  Basic models of ANN  Learning methods  Activation functions  Important terminologies of ANN: Weights  Bias  Threshold  Learning Rate  Momentum factor  Vigilance parameters. Practical Assignments:
 
Unit2 
Teaching Hours:15 
Supervised Learning Algorithms


Concept of supervised learning algorithms  Perceptron networks  Adaptive linear neuron (Adaline)  Multiple adaptive linear neuron  BackPropagation network: Learning factors  Initial weights  Learning rate ɑ  Momentum factor  Generalization  Training and testing of the data. Practical Assignments: 3. Exercise on multiple adaptive linear neurons  
Unit3 
Teaching Hours:15 
Unsupervised Learning Algorithms


Concept of unsupervised learning algorithms  Fixed weight competitive net: Maxnet  Mexican Hat net  Hamming networks  Kohonen selforganizing feature maps  Learning vector quantization. Practical Assignments: 5. Exercise on Maxnet and Mexican Hat net.  
Unit4 
Teaching Hours:15 
Convolution Neural Networks


Introduction  Components of Convolution Neural Networks (CNN) architecture: Padding  Strides  Rectified linear unit layer  Exponential linear unit  Pooling  Fully connected layers  Local response normalization  Hierarchical feature engineering  Training CNN using Backpropagation through convolutions  Case studies: AlexNet  GoogLeNet. Practical Assignments: 9. Exercise on building CNN with the rectified linear unit and exponential linear unit  
Unit5 
Teaching Hours:15 
Deep Reinforcement Learning


Stateless algorithms: Naive algorithms  Upper bounding methods  Simple reinforcement learning for TicTacToe  StrawMan algorithms  Bootstrapping for value function learning  One policy versus off policy methods: SARSA  Policy gradient methods: Finite difference method  Likelihood ratio method  Monte Carlo tree search. Practical Assignments: 13. Exercise on Naive and upper bounding algorithms for data classification.  
Text Books And Reference Books:
 
Essential Reading / Recommended Reading
 
Evaluation Pattern CIA  50% ESE  50%  
MST471B  SPATIAL STATISTICS (2020 Batch)  
Total Teaching Hours for Semester:75 
No of Lecture Hours/Week:5 
Max Marks:150 
Credits:4 
Course Objectives/Course Description 

This course has been conceptualized in order to understand the fundamental and applied concepts of spatial statistics that describe the diverse set of methods to model and analyze the various types of Spatial data. 

Learning Outcome 

By the end of the course, the learner will be able to: CO1: Demonstrate an understanding of the fundamental concepts of spatial statistical analysis. CO2: Identify the various types of spatial data by plots. CO3: Apply the appropriate statistical model to the various types of spatial data. CO4: Analyze and interpret the spatial data problems of various disciplines. 
Unit1 
Teaching Hours:15 
Introduction to spatial statistics


Spatial data  Types of spatial data Geostatistical data, Lattice data, Point pattern data with examples  Visualizing spatial data: Traditional plots, lattice plots and interactive plots – Exploratory spatial data analysis  Intrinsic stationarity, SquareRootDifferences Cloud  The Pocket plot – Decomposing the data into large and small scale variation  Analysis of residuals – Variogram of residuals. Practical Assignments:
 
Unit2 
Teaching Hours:15 
Geostatistical data


Stationary Processes: Variogram, Covariogram and Correlogram  Estimation of variogram: Comparison of the variogram and covariogram estimation, exact distribution theory of the variogram  Robust estimation of variogram – Spectral representations: Valid covariograms and variograms  Variogram model fitting: Criteria for fitting a variogram model, properties of variogramparameter estimators, Crossvalidating the fitted variogram. Practical Assignments:
 
Unit3 
Teaching Hours:15 
Spatial prediction and kriging


Scale of variation  Ordinary Kriging: Effect of variogram parameters on Kriging, Lognormal and TransGaussian Kriging, Cokriging – Robust Kriging – Universal Kriging : Estimation of variogram for Universal Kriging – MedianPolish Kriging: Gridded and nongridded data, Median Polishing spatial data, Bias in MedianBased covariogram estimators – Applications of Geostatistics. Practical Assignments:
 
Unit4 
Teaching Hours:15 
Spatial models on lattice data


Lattices – Spatial data analysis, Trend removal  Conditionally and simultaneously specified spatial gaussian models – Markov random fields – Conditionally specified spatial models for discrete and continuous data – Parameter estimation for Lattice models using gaussian maximum likelihood estimation– Properties of estimators – Statistical image analysis and remote sensing. Practical Assignments:
 
Unit5 
Teaching Hours:15 
Spatial point patterns


Spatial point patterns data analysis: Complete spatial randomness, regularity and clustering – Kernel estimators of intensity function – Distance methods: NearestNeighbor methods – Statistical spatial analysis of point processes: Stationary and Isotropic point processes – Palm distribution – Models and model fitting: Inhomogeneous Poisson, Cox and Poisson cluster process Practical Assignments:
 
Text Books And Reference Books: 1. Cressie, Noel A.C. (2015). Statistics for Spatial Data. Revised Edition. Wiley Interscience Publication.  
Essential Reading / Recommended Reading 1. Bivand Roger S., Pebesma Edzer J. and GomezRubio V. (2013). Applied Spatial Data Analysis with R. Springer New York(2nd Edition).  
Evaluation Pattern CIA 50%+ESE 50%  
MST471C  BIG DATA ANALYTICS (2020 Batch)  
Total Teaching Hours for Semester:75 
No of Lecture Hours/Week:5 
Max Marks:150 
Credits:4 
Course Objectives/Course Description 

This course has been designed to train the students in handling different types of Big data sets and provide knowledge about the methods of handling these types of data sets. 

Learning Outcome 

By the end of the course, the learner will be able to: CO1: Demonstrate the understanding of basic concepts of Big data CO2: Identify different types of Hadoop architecture CO3: Illustrate the parallel processing of data using MapReduce techniques CO4: Analyze the Big data under Spark architecture CO5: Demonstrate the programming of Big data using Hive and Pig environments 
Unit1 
Teaching Hours:15 
Introduction


Concepts of Data Analytics: Descriptive, Diagnostic, Predictive, Prescriptive analytics Big Data characteristics: Volume, Velocity, Variety, Veracity of data  Types of data: Structured, Unstructured, SemiStructured, Metadata  Big data sources: HumanHuman communication, HumanMachine Communication, MachineMachine Communication  Data Ownership  Data Privacy. Practical Assignments: 1. Setting up infrastructure and Automation environment 2. Case study for identifying Data Characteristics  
Unit2 
Teaching Hours:15 
Big Data Architecture


Standard Big data architecture  Big data application  Hadoop framework  HDFS Design goal  MasterSlave architecture  Block System  Readwrite Process for data  Installing HDFS  Executing in HDFS: Reading and writing Local files and Data streams into HDFS  Types of files in HDFS  Strengths and alternatives of HDFS  Concept of YARN.
Practical Assignments: 3. Exercise on Installing HDFS 4. Exercise on Reading and Writing Local files into HDFS 5. Exercise on Reading and Writing Data streams into HDFS
 
Unit3 
Teaching Hours:15 
Parallel Processing with MapReduce


Introduction to MapReduce  Sample MapReduce application: Wordcount  MapReduce Data types and Formats  Writing MapReduce Programming  Testing MapReduce Programs  MapReduce Job Execution  Shuffle and Sort  Managing Failures  Progress and Status Updates. Practical Assignments: 6. Exercise on MapReduce applications 7. Exercise on writing and testing MapReduce Programs 8. Exercise on Shuffle and Sort 9. Exercise on Managing Failures  
Unit4 
Teaching Hours:15 
Stream Processing with Spark


Stream processing Models and Tools  Apache Spark  Spark Architecture: Resilient Distributed Datasets, Directed Acyclic Graph  Spark Ecosystem  Spark for Big Data Processing: MLlib, Spark GraphX, SparkR, SparkSQL, Spark Streaming  Spark versus Hadoop Practical Assignments: 10. Exercise on installing Spark 11. Exercise on Directed Acyclic Graph 12. Exercise on Spark using MLlib, Spark GraphX 13. Exercise on Spark using SparkR, Spark Streaming  
Unit5 
Teaching Hours:15 
Hive and Pig


Hive Architecture  Components  Data Definition  Partitioning  Data Manipulation  Joins, Views and Indexes  Hive Execution  Pig Architecture  Pig Latin Data Model  Latin Operators  Loading Data  Diagnostic Operators  Group Operators  Pig Joins  Row Level Operators  Pig Builtin function  Userdefined functions  Pig Scripts. Practical Assignments: 14. Exercise on Hive Architecture 15. Exercise on Pig Architecture
 
Text Books And Reference Books:
 
Essential Reading / Recommended Reading
 
Evaluation Pattern CIA  50% ESE  50%  
MST472A  HIGH DIMENSIONAL STATISTICAL ANALYSIS (2020 Batch)  
Total Teaching Hours for Semester:75 
No of Lecture Hours/Week:5 
Max Marks:150 
Credits:4 
Course Objectives/Course Description 

This course has been conceptualized in order to understand the high dimensional data and the statistical techniques such as principal component analysis, multidimensional scaling, independent component analysis and projection pursuit that are used to analyze the most challenging multidimensional real life problems. 

Learning Outcome 

By the end of the course, the learner will be able to: CO1: Identify high dimensional problems in various domains. CO2: Select the appropriate statistical techniques to analyze high dimensional data. CO3: Apply the various statistical techniques to analyze the high dimensional real life problems. CO4: Interpret the results obtained by high dimensional statistical analysis in the context of real world problems. 
Unit1 
Teaching Hours:12 
Unit I: Understanding high dimensional data


Introduction to high dimensional data: high dimensional data in various fields with examples  need of high dimensionality  Curse and blessings of Dimensionality  Visualization of multidimensional data  parallel coordinate plots  multivariate random vectors  Multivariate normal distribution and estimation of parameters using likelihood estimation. Practical Assignments: 1. Exercise on visualization of high dimensional data 2. Exercise on multivariate normal distribution  
Unit2 
Teaching Hours:18 
Principal component analysis in high dimensions


Principal component analysis  Principal components and dimension reduction  Visualization of principal components  Scree, Score, Projection plots and estimates of the density of the scores  Properties of principle components  Uses and interpretation of principal components  Standardized and high dimensional data  Sparse principal component analysis with LASSO and elastic nets  Consistency of principal components as the dimension grows.
Practical Assignments:
3. Exercise on the identification of principal components.
4. Exercise on projection plots.
5. Exercise on sparse principal component analysis based on LASSO.
6. Exercise on sparse principal component analysis based on elastic nets.
 
Unit3 
Teaching Hours:15 
Multidimensional scaling


Classical scaling  Classical scaling with principal coordinates  Classical scaling with strain Metric and nonmetric scaling  Scaling for highdimensional data and relationships between different configurations of the same data  Procrustes rotations and individual differences scaling  Scaling for grouped and count data  Corresponding Analysis  Analysis of Distance  Low  Dimensional Embeddings. Practical Assignments: 7. Exercise on principal coordinate analysis 8. Exercise on metric scaling 9. Exercise on nonmetric scaling 10. Exercise on scaling for high dimensional data 11. Exercise on corresponding analysis 12. Exercise on analysis of distance  
Unit4 
Teaching Hours:18 
Independent component analysis to high dimensional data


Independent component analysis  Introduction, sources and signals, identification of sources  Mutual information and Gaussianity  Estimation of the mixing matrix  NonGaussianity and independence in practice  Independent Component Scores and solutions Independent component solutions for real and simulated data  Low dimensional projections for high dimensional data  Dimension selection with independent components. Practical Assignments: 13. Exercise on independent component analysis for real data 14. Exercise on independent component analysis for simulated data 15. Exercise on low dimensional projections for high dimensional data 16. Exercise on dimension selection with independent components  
Unit5 
Teaching Hours:12 
Projection pursuit to high dimensional data


Projection Pursuit with one, two and three dimensional projections  Comparison of projection pursuit with independent component analysis  Projection pursuit density estimation and regression. Practical Assignments: 17. Exercise on comparison of projection pursuit with independent component analysis 18. Exercise on projection pursuit regression  
Text Books And Reference Books: 1. Inge Koch (2013). Analysis of multivariate and highdimensional data. Cambridge University Press  
Essential Reading / Recommended Reading Wainwright, Martin, J. (2019). HighDimensional StatisticsA NonAsymptotic Viewpoint. Cambridge University Press. 2. Giraud, C. (2014). Introduction to HighDimensional Statistics. CRC Press.  
Evaluation Pattern CIA50% ESE50%  
MST472B  STATISTICAL GENETICS (2020 Batch)  
Total Teaching Hours for Semester:75 
No of Lecture Hours/Week:5 
Max Marks:150 
Credits:4 
Course Objectives/Course Description 

To enable the students to understand and apply different concepts of statistical genetics in large populations with selection, mutation and migration. The students would be exposed to the physical basis of inheritance, detection and estimation of linkage, estimation of genetic parameters and development of selection indices. 

Learning Outcome 

By the end of the course, the learner will be able to: CO1: Describe basic concepts of estimation of linkage and segregation in large populations. CO2: Demonstrate the effect of systematic forces on change of gene frequency. CO3: Estimate genetic variance and analyse its partitioning CO4: Apply statistical methodology to estimate the correlation between relatives and selection index CO5: Interpret the results of various statistical genetics techniques. 
Unit1 
Teaching Hours:15 
Segregation and Linkage


Physical basis of inheritance  Analysis of segregation  Detection and Estimation of linkage for qualitative characters  Amount of information about linkage  Combined estimation  Disturbed segregation. Practical Assignments: 1. Analysis of segregation, detection and estimation of linkage. 2. Estimation of Amount of information about linkage. 3. Calculation of combined estimationof linkage.  
Unit2 
Teaching Hours:15 
Equilibrium law and SexLinked gene


Gene and genotypic frequencies  Random mating and HardyWeinberg law  Application and extension of the equilibrium law  Fisher’s fundamental theorem of natural selection  Disequilibrium due to linkage for two pairs of genes  Sex  Linked genes. Practical Assignments: 4. Estimation of disequilibrium due to linkage for two pairs of genes. 5. Estimation of path coefficients. 6. Estimation of equilibrium between forces in large populations.  
Unit3 
Teaching Hours:15 
Systematic forces


Forces affecting gene frequency: Selection  Mutation and Migration  Equilibrium between forces in large populations  Polymorphism. Practical Assignments: 7. Estimation of changes in gene frequency due to systematic forces. 8. Estimation of the Inbreeding coefficient.  
Unit4 
Teaching Hours:15 
Genetic variance and its partitioning


Polygenic system for quantitative characters  Concepts of breeding value and Dominance deviation  Genetic variance and its partitioning. Practical Assignments: 9. Analysis of genetic components of variation. 10. Estimation of breeding values.  
Unit5 
Teaching Hours:15 
Association and Selection index


Correlation between relatives – Heritability  Repeatability and Genetic correlation  Response due to selection  Selection index and its applications in plants and animals improvement Programme  Correlated response to selection  Restricted selection index  Inbreeding and crossbreeding  Changes in mean and variance. Practical Assignments: 11. Estimation of Heritability and repeatability coefficient, 12. Estimation of the genetic correlation coefficient.  
Text Books And Reference Books: 1. Jain, J.P. (2017). Statistical Techniques in Quantitative Genetics. Tata McGraw  
Essential Reading / Recommended Reading 1.Laird N.M and Christoph, L. (2011). The Fundamental of Modern Statistical Genetics. Springer. 2. Balding DJ, Bishop, M. and Cannings, C. (2001). Handbook of Statistical Genetics. John Wiley. 3. Shizhong Xu.(2013). Principles of Statistical Genomics. Springer. 4.Falconer, D.S. (2009). Introduction to Quantitative Genetics. English Language Book Society. Longman. Essex.  
Evaluation Pattern CIA  50 % ESE 50 %  
MST472C  ACTUARIAL METHODS (2020 Batch)  
Total Teaching Hours for Semester:75 
No of Lecture Hours/Week:5 
Max Marks:150 
Credits:4 
Course Objectives/Course Description 

This course is designed to equip students with the knowledge of actuarial models and their applications 

Learning Outcome 

By the end of the course students will be able to: CO1: Demonstrate the understanding of basic concepts of actuarial methods. CO2: Identify various actuarial models. CO3: Illustrate survival models and life tables. CO4: Interpret the reallife data based on exploratory data analysis. CO5: Apply actuarial models to reallife data. 
Unit1 
Teaching Hours:15 
Introduction to actuarial statistics


Utility theoryintroduction  insurance and utility theory  models for individual claims and their sums  curtate future lifetime  the force of mortality assumptions for fractional ages  some analytical laws of mortality  multiple life functions  joint life and last survivor status  insurance and annuity benefits through multiple life functions  evaluation for special mortality laws. Practical Assignments: 1. Problems based on multiple life functions 2. Illustrate discrete and continuous annuity benefits  
Unit2 
Teaching Hours:15 
Survival analysis and life tables


Introduction to survival analysis  life table and its relation with survival function  examples  assumptions for fractional ages  estimate empirical survival and loss distribution using KaplanMeier estimator  Nelson Aalen estimator  Cox proportional hazards and Kernel density estimators. Practical Assignments: 3. Apply survival models to simple problems in longterm insurance, pensions and banking. 4. Preparation of life tables based on the real life data. 5. Estimation of survival distribution using KaplanMeier estimator, Nelson Aalen estimator, Cox proportional hazards and Kernel density estimators  
Unit3 
Teaching Hours:15 
Actuarial models


Principles of actuarial modelling  stochastic and deterministic models  their advantages and disadvantages  frequency models: distributions suitable for modelling frequency of losses (Poisson, Binomial, negative binomial and geometric distributions)  fundamentals of aggregate models  computation of aggregate claims distributions and calculation of loss probabilities  evaluate the effect of coverage modifications (deductibles, limits and coinsurance)  inflation on aggregate models. Practical Assignments: 6. Compute relevant moments, probabilities and other distributional quantities for collective risk models. 7. Compute aggregate claims, distributions and use them to calculate loss probabilities. 8. Evaluate the effect of coverage modifications and inflation on aggregate models.  
Unit4 
Teaching Hours:15 
Insurance and Annuities


Principles of compound interest Nominal and effective rates of interest and discount  the force of interest and discount  compound interest  accumulation factor  continuous  compounding  life insurance  life annuities  net premiums  net premium reserves  some practical considerations  premiums that include expenses  general expenses  types of expenses  per policy expenses  claim amount distributions  approximating the individual model  stoploss insurance. Practical Assignments: 9. Illustrate discrete and continuous insurance benefits 10. Illustrate discrete and continuous annuity benefits
 
Unit5 
Teaching Hours:15 
Data and Systems


Data as a resource for problemsolving  exploratory data analysis: single and multiple linear regression principal component analysis and survival analysis  statistical learning: difference between supervised and unsupervised learning  professional and risk management issues  ethical and regulatory issues involved in using personal data and extremely large data sets  visualizing data and reporting. Practical Assignments: 11. Apply principal component analysis to reduce the dimensionality of a complex data set. 12. Fit simple and multiple linear models to a data set and interpret the results. 13. Fit a survival model to a data set and interpret the output.  
Text Books And Reference Books:
 
Essential Reading / Recommended Reading 1. Zdzislaw Brzezniak and Tomasz Zastawniak (2000), Basic stochastic processes: A course through exercises. Springer. 2. Grimmett Geoffery and David Stizaker (2001), Probability and random processes. Oxford University Press. 3. J. Medhi, Stochastic Processes (2009), John Wiley.  
Evaluation Pattern CIA  50% ESE  50%  
MST473A  BAYESIAN STATISTICS (2020 Batch)  
Total Teaching Hours for Semester:75 
No of Lecture Hours/Week:5 
Max Marks:150 
Credits:4 
Course Objectives/Course Description 

Students who complete this course will gain a solid foundation in how to apply and understand Bayesian statistics and how to understand Bayesian methods vs frequentist methods. Topics covered include: an introduction to Bayesian concepts; Bayesian inference for binomial proportions, Poisson means, and normal means; modelling 

Learning Outcome 

By the end of the course, the learner will be able to: CO1: Identify Bayesian methods for a binomial proportion and a Poisson mean CO2: Perform Bayesian analysis for differences in proportions and means CO3: Analyse normally distributed data in the Bayesian framework CO4: Evaluate posterior distribution using various sampling procedures. CO5: Compare Bayesian methods and frequentist methods

Unit1 
Teaching Hours:15 
Introduction to Bayesian Thinking


Basics of minimaxity  subjective and frequentist probability  Bayesian inference  prior distributions  posterior distributions  loss function  the principle of minimum expected posterior loss  quadratic and other common loss functions  advantages of being Bayesian  Improper priors  common problems of Bayesian inference  Point estimators  Bayesian confidence intervals, testing  credible intervals Practical Assignments: 1.Construction of prior, conditional and posterior probabilities for the chosen data set 2.Computation minimum expected posterior loss. 3.Computation of Bayesian confidence intervals.
 
Unit2 
Teaching Hours:15 
Bayesian Inference for Discrete Random Variables


Two Equivalent Ways of Using Bayes' Theorem  Bayes' Theorem for Binomial with Discrete Prior  Important Consequences of Bayes' Theorem  and Bayes' Theorem for Poisson with Discrete prior. Practical Assignments: 4.Bayes Classification 5.Examples of Binomial distribution with discrete prior. 6.Examples of Poisson distribution with discrete prior.
 
Unit3 
Teaching Hours:15 
Bayesian Inference for Binomial Proportion


Using a Uniform Prior  Using a Beta Prior  Choosing Your Prior  Summarizing the Posterior Distribution  Estimating the Proportion  Bayesian Credible Interval Comparing Bayesian and Frequentist Inferences for Proportion: Frequentist Interpretation of Probability and Parameters  Point Estimation  Comparing Estimators for Proportion  Interval Estimation  Hypothesis Testing  Testing a OneSided Hypothesis  Testing a TwoSided Hypothesis. Bayesian Inference for Poisson: Some Prior Distributions for Poisson  Inference for Poisson Parameter. Practical Assignments: 7.Estimation of binomial proportion using uniform prior distribution. 8.Estimation of binomial proportion using beta prior distribution. 9.Estimation of Poisson parameter using some prior distributions
 
Unit4 
Teaching Hours:15 
Bayesian Inference for Normal Mean


Bayes' Theorem for Normal Mean with a Discrete Prior  Bayes' Theorem for Normal Mean with a Continuous Prior  Normal Prior, Bayesian Credible Interval for Normal Mean  Predictive Density for Next Observation. Practical Assignments: 10.Bayes estimator for Normal Mean with a Discrete Prior. 11.Bayes estimator for Normal Mean with a Continuous Prior. 12.Bayes Credible interval for the normal mean.
 
Unit5 
Teaching Hours:15 
Bayesian Computations


Analytic approximation  EM Algorithm  Monte Carlo sampling  Markov Chain Monte Carlo Methods  MetropolisHastings Algorithm  Gibbs sampling: examples and convergence issues. Practical Assignments: 13.EM algorithm. 14.MonteCarlo sampling. 15.Gibbs Sampling. 16.Markov Chain MonteCarlo application.
 
Text Books And Reference Books: 1. Bolstad W. M. and Curran, J.M. (2016) Introduction to Bayesian Statistics 3rd Edition. Wiley, New York 2. Jim, A. (2009). Bayesian Computation with R, 2nd Edition, Springer.
 
Essential Reading / Recommended Reading 1. Berger, J.O. (1985a). Statistical Decision Theory and Bayesian Analysis, 2nd Ed. SpringerVerlag, New York. 2. Christensen R, Johnson, W., Branscum, A. and Hanson T. E. (2011). Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians, Chapman & Hall. 3. Congdon, P. (2006). Bayesian Statistical Modeling, Wiley 4. Ghosh, J. K., Delampady M. and T. Samantha (2006). An Introduction to Bayesian Analysis: Theory & Methods, Springer. 5. Rao. C.R. and Day. D. (2006). Bayesian Thinking, Modeling & Computation, Handbook of Statistics, Vol. 25. Elsevier.
 
Evaluation Pattern CIA 50% ESE 50%  
MST473B  CLINICAL TRIALS (2020 Batch)  
Total Teaching Hours for Semester:75 
No of Lecture Hours/Week:5 
Max Marks:150 
Credits:4 
Course Objectives/Course Description 

This course is designed to train the students in the design and conduct of clinical trials and provide knowledge about the methods of statistical data analysis of clinical trials. 

Learning Outcome 

By the end of the course, the learner will be able to: CO1: Understand the study designs of randomized clinical trials CO2: Apply statistical principles, concepts and methods for the analysis of data in clinical trials CO3: Demonstrate competencies in evaluating clinical research data and communicating results CO4: Demonstrate advanced critical thinking skills necessary to advance within the biopharmaceutical industry. 
Unit1 
Teaching Hours:15 
Introduction to Clinical Trials


Historical background of clinical trials  the need for clinical trials  ethics and planning of clinical trials  main features of study protocol  the selection of study subjects  treatment schedule  evaluation of patient response  followup studies  GCP/ICH guidelines Practical Assignments:
 
Unit2 
Teaching Hours:15 
Phases of clinical trials


Different phases of clinical trials: phase I, phase II, phase III, phase IV  Basic study designs randomized controlled trials  nonrandomized concurrent controlled trials  historical controls  cross over design  withdrawal design  hybrid designs  group allocation designs and studies of equivalency. Practical Assignments:
 
Unit3 
Teaching Hours:15 
Methods of randomization


Fixed allocation randomization  stratified randomization  adaptive randomization  unequal randomization  Intervention and placebos  blinding in clinical trials: unblended trials  singleblind trials  doubleblind trials and tripleblind trials.
Practical Assignments:
 
Unit4 
Teaching Hours:15 
Estimation of sample size for clinical trials


Various methods for determining sample size for clinical trials: method for dichotomous response variable  continuous response variable  repeated measures  cluster randomization and equivalency of intervention  Multicenter trials. Practical Assignments:
 
Unit5 
Teaching Hours:15 
Data management


Design of case report form  data collection  intention to treat analysis and perprotocol analysis  interim analysis  reporting adverse events  issues in data analysis  nonadherence  poor quality and missing data Practical Assignments: 11. Exercise on intention to treat analysis 12. Exercise on per protocol analysis 13. Exercise on handling missing data in the analysis  
Text Books And Reference Books:
 
Essential Reading / Recommended Reading
 
Evaluation Pattern CIA  50% ESE 50%  
MST473C  RISK MODELING (2020 Batch)  
Total Teaching Hours for Semester:75 
No of Lecture Hours/Week:5 
Max Marks:150 
Credits:4 
Course Objectives/Course Description 

This course will equip students with a wide variety of statistical methods for modelling risk. 

Learning Outcome 

By the end of the course, the learner will be able to: CO1: Demonstrate the understanding of basic concepts of risk modelling CO2: Apply probabilistic concepts for modelling risk CO3: Analyse risk using statistical doseresponse models CO4: Apply risk management to individual portfolio problems 
Unit1 
Teaching Hours:12 
Basic Risk Models


Distinguishing Characteristics Of Risk Analysis  Traditional Health Risk Analysis  Defining Risks: Source, Target, Effect, Mechanism  Basic Quantitative Risk Models  Risk as Probability of a Binary Event  Hazard Rate Models Practical Assignments: 1. Lab exercise on the quantitative risk model. 2.. Lab exercise on the hazard rate model  
Unit2 
Teaching Hours:18 
Risk Assessment Modelling


Conditional Probability Framework for Risk Calculations  Population Risks Modeled by Conditional Probabilities  Trees, Risks and Martingales  Compartmental Flow Simulation Models  Monte Carlo Uncertainty Analysis  Introduction to Exposure Assessment  Uncertainty Analysis Practical Assignments: 3. Lab exercise on risk calculations. 4. Lab exercise on risk modelling by conditional probabilities. 5. Lab exercise on compartment flow simulation model. 6. Lab exercise on Monte Carlo uncertainty analysis  
Unit3 
Teaching Hours:15 
Advanced Statistical Risk Modelling


Statistical DoseResponse Modeling  Exposure and Response Variables  Risk, Confidence Limits, and Model Fit  Model Uncertainty and Variable Selection  Dealing with Missing Data
Practical Assignments: 7. Lab exercise on DoseResponse modelling. 8. Lab exercise on the estimation of risk and confidence limit. 9. Lab exercise on variable selection procedures. 10. Lab exercise on missing data algorithms  
Unit4 
Teaching Hours:17 
Causality


Statistical vs Causal Risk Modeling  Criteria for Causation  Epidemiological Criteria for Causation  Criteria for Inferring Probable Causation  Causal Graph Models and Knowledge Representation  Testing Hypothesized Causal Graph Structures  Causal Graphs in Risk Analysis  Probabilistic Inferences in DAG Models  Using DAG Models to Make Predictions Practical Assignments: 11. Lab exercise on causal risk models. 12. Lab exercise on causal graph models. 13. Lab exercise on Testing Hypothesized Causal Graph Structures. 14. Lab exercise on DAG models
 
Unit5 
Teaching Hours:13 
Individual Risk Management Decisions


Value Functions and Risk Profiles  Rational Individual RiskManagement via Expected Utility  EU DecisionModeling Basics  DecisionMaking Algorithms and Technologies  Axioms for EU Theories  Cognitive Heuristics and Biases Violate Reduction  Subjective Probability and Subjective Expected Utility (SEU) Practical Assignments: 15. Lab exercise on EU decision modelling. 16. Lab exercise on optimization of decisionmaking algorithms  
Text Books And Reference Books:
 
Essential Reading / Recommended Reading
 
Evaluation Pattern CIA  50% ESE  50%  
MST481  SEMINAR PRESENTATION (2020 Batch)  
Total Teaching Hours for Semester:30 
No of Lecture Hours/Week:2 
Max Marks:50 
Credits:1 
Course Objectives/Course Description 

This course is to enhance the verbal and written presentation skills of students and to develop analytical skills as students learn new areas and ideas in Statistics. 

Learning Outcome 

By the end of the course, the learner will be able to, CO1: Demonstrate presentation and writing skills.

Unit1 
Teaching Hours:30 
Presentation


1. Prepare a report on a relevant topic. 2. Present it well before the class and panel members.
 
Text Books And Reference Books: _  
Essential Reading / Recommended Reading _  
Evaluation Pattern CIA 50% ESE 50% 